Abstract: In this paper, a solution procedure of the finite element incremental analysis for material nonlinear problems is presented. The procedure includes the predicted secont stiffness constitutive relations, Bergan's method regarding automatic selection of load increments and the evaluation of the results obtained. Then two numerical examples of thick-wall cylinders with perfectly plastic and power strain-hardening materials are given and comparisions are made among the theoretical results and the results from the first order self-correcting procedure, Chang's predictor-corrector procedire with asympototic integration of elastoplastic constitutive relations and the prodicted secont stiffness procedure.The results show that the procedure in this paper can improve the computational precisi onand/or the computational efficience,and has the same function of self-correcting as the first order self-correcting procedure does.Finaly suggestions are made that the ideas in the paper may be used for BEM and asympototic integration procedure for elastoplastic incremental analyses in which linearized stress-strain curves are assumed.