The scope of this work comprises of the study of mathematical nature of this code model and to predict the accuracy of the model in nuclear reactor safety analysis. Method of characteristics is applied to check the non-hyperbolic nature of conservation equations for all normal and accident conditions of LWR. The analysis also gives information about the soundness of the model and to identify the regions where the solutions obtained from it will be numerically convergent. The characteristics of equations of non-hyperbolic nature are complex. It implies that results thus obtained (by finite difference method) have to be interpreted very carefully in view of the sensitive nature of reactor safety analysis. The present analysis shows that governing equations of the code exhibit complex characteristics for some operating conditions thus implying non-hyperbolicity under those conditions. Results are less accurate under such conditions, so sensitivity analysis plays an important role. The sensitivity of closure relationship on conservation equation's stability is also checked. The analysis is performed in MATLAB environment for four different systems, (a) a simplified vertical pipe (b) Pressurized Water Reactor (PWR, 15.5 MPa), (c) Boiling Water Reactor (BWR, Pressure 7.0 MPa ) and (d) Natural circulation reactor (AHWR, pressure 0.7 MPa). These results can also be extended for other thermal hydraulic systems.The importance of method of characteristics (in reactor thermal safety analysis) is clearly evident here.