Abstract: The Element Energy Projection (EEP) method for super-convergent calculation in the post-process of FEM and the corresponding EEP-based self-adaptive FEM have achieved remarkable success in 1D variational inequality problems. In this paper, the EEP-based self-adaptive FEM for 2D variational inequality problems has been successfully developed. Two novel techniques, i.e. 2D bisection bounding technique and 2D C-check technique, are proposed, which significantly accelerate the convergence rate of the conventional relaxation iteration in finite element (FE) procedures. Once the converged FE solution is obtained, the super-convergent solution via the EEP method, developed by the first author's research team, will be calculated to estimate the FE errors and then to guide mesh refinement. Numerical examples presented show that the proposed algorithm is efficient, reliable, and accurate with the final results being virtually ‘numerically exact', i.e. satisfying the error tolerance by the maximum norm.