Abstract: Based on the parametric variational principle, a quadratic programming method is developed for the elastic-plastic finite element analysis of a 3D Cosserat continuum model. Since the classical continuum model which is lack of internal scale parameter suffers from pathological mesh dependence in the strain localization analysis, the governing equations of the Cosserat continuum model are regularized by adding a rotational degrees-of-freedom and internal scale parameters to the conventional continuum model. Numerical examples are calculated to demonstrate the efficiency of the 3D Cosserat finite element model and the stability of the proposed computational algorithm for numerical simulation of strain localization problems. Particularly, the mesh independent results are ensured.