A review of numerical procedures for stress calculation in the inelastic finite element analysis is presented. The role of stress integration within a time (load) step in the incremental-iterative scheme for the displacements based FE formulation is first given briefly. Then, the basic relations of the explicit algorithms, as the first ones developed in the 70s, are presented. The shortcomings of these algorithms are pointed out. The implicit procedures are presented in some detail, with the emphasis on a general return mapping procedure and the governing parameter method (GPM). Derivation of the consistent tangent moduli represents an important task in the inelastic FE analysis because the overall equilibrium iteration rate depends on these moduli. The basic concepts of this derivation are presented. An important field, very challenging in today’s stage of design and technology, is the large strain deformation of material. A review of the approaches in the large strain domain that includes the rate and the total formulations is given in some detail. Special attention is devoted to the multiplicative decomposition of deformation gradient concept, since that concept is generally favored today. Some unresolved issues, such as the use of the stress and strain measures, are discussed briefly. A number of selected numerical examples illustrate the main topics in the stress integration task, as well as the applications of the stress integration algorithms to various material models. Some concluding remarks and an outline of further research topics are given at the end of the paper. This review article includes 205 references.

*Computational Inelasticity*, Springer-Verlag, NY.

*Finite Element Procedures in Engineering Analysis*, Prentice-Hall, Englewood Cliffs, NJ.

*Finite Element Procedures*, Prentice-Hall, Englewood Cliffs, NJ.

*Computational Procedures in Inelastic Analysis of Solids and Structures*, Center Sci Res Serbian Academy Sci Art and Univ Kragujevac, Kragujevac, Serbia.

*Inelastic Analysis of Solids and Structures*, Springer-Verlag, Berlin-Heidelberg, to be published.

*Plasticity: Theory and Application*, The Macmillan Co, NY.

*Finite Elements in Plasticity: Theory and Practice*, Pineridge Press, Swansea, UK.

*Plasticity for Structural Engineers*, Springer-Verlag, NY.

*Constitutive Laws for Engineering Materials*, Prentice-Hall, Englewood Cliffs, NJ.

*Nonlinear Analysis in Soil Mechanics*, Elsevier, Amsterdam.

*Soil Behavior and Critical State Soil Mechanics*, Cambridge Univ Press, Cambridge.

*Numerical and Computer Methods in Structural Mechanics*, SJ Fendes (ed), Academic Press, NY.

*Design for Creep*, McGraw-Hill, London.

*Creep and Fatigue in Elevated Temperature Applications*,

**1**Mech Eng Publ, London, 157, 1–9.

*Pressure Vessel Technology, Vol. 1, Design and Analysis*, ASME, NY, 418–442.

*Methods in Computational Physics*

**3**, B Alder (ed), Academic Press, New York and London, 211–263.

*Computational Plasticity Models, Software, and Applications*,

*Vol 1*, DRJ Owen et al. (eds), Pineridge Press, Swansea, 133–159.

*Proc of 2nd Berkeley Symp on Mathematical Statistics and Probability*, J Neyman (ed), Univ California Press, Berkeley and LA, 481–492.

*Progress in Solid Mechanics*, S Sneddon and R Hill (eds), North-Holland, Amsterdam, pp. 165.

*Proc of Int Conf on Computer-Aided Analysis and Design of Concrete Structures I*, F Damjanic et al. (eds), Pineridge Press, Swansea, UK, 289–299.

*A General Concept for Implicit Stress Integration of Inelastic Constitutive Relations*, (in Serbian), Center Sci Res Serbian Academy Sci Art and Univ Kragujevac, Kragujevac, Serbia.

*Proc of Int Conf on Comput Plasticity, COMPLAS III*, Pineridge Press, Swansea, UK.

*Computational Plasticity*, DRJ Owen and E Onate (eds), Pineridge Press, Swansea, UK, 249–259.

*Computational Plasticity*, DRJ Owen, E Onate, and E Hinton (eds), CIMNE, Barcelona, 1691–1695.

*Computational Plasticity*, DRJ Owen and E Onate (eds), Pineridge Press, Swansea, UK, 1809–1820.

*IASS-IACM 2000 4th Int Coll Comput Shell Spat Struct*, June 5–7 2000, Chania-Crete, Greece.

*IASS-IACM 2000 4th Int Coll Comput Shell Spat Struct*, June 5–7 2000, Chania-Crete, Greece.

*Advances in Applied Mechanics*, CS Yih (ed),

**18**, Academic Press, NY, 1–75.

*Theoretical Foundation for Large-Scale Computations of Nonlinear Material Behavior*, S Nemat-Nasser, RJ Assaro, and GA Hegemier (eds), Matrinus Nijhoff Pub, 99–108.

*Constitutive Equations in Viscoplasticity: Computational and Engineering Aspects*, Winter Annual Meeting of ASME, NY.

*Non-Linear Elastic Deformations*, Ellis Horwood, Chichester, England.

*Numerical Analysis of Forming Processes*, JF Pitman, OC Zienkiewicz, RD Wood, and JM Alexander (eds), J Wiley & Sons Ltd, 351–371.

*Theoretical Foundation for Large-Scale Computations of Nonlinear Material Behavior*, S Nemat-Nasser, RJ Assaro, and GA Hegemier (eds), Matrinus Nijhoff Pub, 7–24.

**23.**

*Finite Inelastic Deformations—Theory and Applications*, D Besdo and E Stain (eds), Springer-Verlag, Berlin-Heidelberg, 300–309.

*Finite Inelastic Deformations—Theory and Applications*, D Besdo and E Stein (eds), Springer-Verlag, Berlin Heidelberg, 363–372.

*Proc. of 4th Greek Natl Congress on Mech*, PS Theocaris and EE Gdoutos (eds), 511–518.

*Finite Element Methods for Nonlinear Problems*, in P Bergan, KJ Bathe, and W Wunderlich (eds), Springer Verlag, Berlin-Heidelberg, 175–190.

*Proc of 12th Conf*, Eng Mech Div ASCE, La Jolla, CA, 1029–1032.

*PAK-S—Program for Linear and Nonlinear Structural Analysis*, Center for Sci Res Serbian Academy Sci Art and Univ Kraguaguj, Serbia.

*An introduction to Mechanics of Solids*, Second Edition, McGraw-Hill Book Co., NY.

*Computational Plasticity*, DRJ Owen, E Onate, and E Hinton (eds), CIMNE, Barcelona, 3–19.

*Finite Inelastic Deformations—Theory and Applications*, D Besdo and E Stein (eds), Springer-Verlag, Berlin Heidelberg, 373–387.

*Computational Plasticity*, DRJ Owen, E Onate, and E Hinton (eds), CIMNE, Barcelona, 178–195.

*Mechanics of Incremental Deformations*, Wiley, New York.

*Finite Inelastic Deformations—Theory and Applications*, D Besdo and E Stein (eds), Springer-Verlag, Berlin Heidelberg, 259–272.

*Computational Plasticity*, DRJ Owen, E Onate, and E Hinton (eds), CIMNE, Barcelona, 635–640.

*IASS-IACM 2000 4th Int Coll Comput Shell Spat Struct*, June 5–7 2000, Chania-Crete, Greece.

*Proc of 2nd Int Conf*, Isehara, Japan, 31 Aug–2 Sept.

*Proc of 3rd Int Conf*, Dearborn, MI, Sept 39–Oct 3.