An implicit computational algorithm for stress integration of the modified Cam-clay model is presented in the paper. The material behavior is described by ellipses with hardening characteristics, and with the critical stress state line. The algorithm is developed for the strain-driven problems and it is employed in the incremental finite element analysis. The problem of stress calculation at the end of a load step is reduced to solution of one nonlinear equation, and the procedure represents an application of the governing parameter method (GPM) developed in Ref. [1]. Hardening and softening plasticity regimes are analyzed in detail. Derivation of the tangent constitutive elastic-plastic matrix, consistent with the stress integration algorithm, is also presented. This matrix provides the quadratic convergence rate in the incremental-iterative finite element analysis. The algorithm is robust, reliable and efficient; and also it provides very good accuracy, illustrated through comparison with solutions available in cited references. It is especially suitable for the displacement based finite element analysis, and it has been implemented in the finite element general purpose program PAK. Typical example of a real bearing capacity problem is solved, with application of the contact algorithm to model interaction between the structure and the soil.