A mesh‐independent finite element method for elastoplastic problems with softening is proposed. The regularization of the boundary value problem is achieved introducing in the yield function the second order gradient of the plastic multiplier. The backward‐difference integrated finite‐step problem enriched with the gradient term is given a variational formulation where the consitutive equations are treated in weak form as well as the other field equations. A predictor–corrector scheme is proposed for the solution of the non‐linear algebraic problem resulting from the finite element discretization of the functional. The expression of the consistent tangent matrix is provided and the corrector phase is formulated as a Linear Complementarity Problem. The effectiveness of the proposed methodology is verified by one‐ and two‐dimensional tests.