According to Hill yield function, the theoretical solutions of limit load of orthotropic cylindrical pipe under different combined loads with internal pressure, axial force, shear force, torsion moment and bending moment have been derived on the basis of elastic perfectly-plastic constitutive model. The effect of radial stress on different combined limit loads of cylindrical pipe is explored and the results show that the radial stress should be considered in the limit load calculation especially for thick-walled cylindrical pipe. For isotropic cylindrical pipe, the limit load increases with the yield strength of the pipe. The limit loads of cylindrical pipe under axial force, pure bending moment, shear force and torsion moment are dependent on the axial yield strength which is equal to the circumferential yield strength. For the orthotropic cylindrical pipe under lower internal pressure, the limit bending moment of the orthotropic cylindrical pipe is primarily decided by the axial yield strength. For the orthotropic cylindrical pipe under higher internal pressure, impact of the circumferential yield strength become obvious. For the orthotropic cylindrical pipe with the same axial yield strength, the circumferential yield strength can enhance the limit load of the pipe under pure axial force, torsion moment and shear force. Under the different combined load conditions of internal pressure, bending moment, axial force, shear force and torsion moment, the variation of the limit bending moment with yield strength ratio is concerned with the load type, the circumferential yield strength and the axial yield strength.