Boundary value problems for a softening material suffer from loss of uniqueness in the post-peak regime. Numerical solutions to such problems shows mesh dependency due to lack of internal length scale in the formulation. A regularization method which introduces a characteristic length is required to get mesh independent results. A second gradient model introduces a characteristic length by taking into account the second gradient of the displacement in the principle of virtual work and thus regularizing the solution of the boundary value problem. In this work a second gradient finite element model has been developed. The regularization property of the method has been studied for elastoplastic and damage constitutive laws. It has been shown that mesh independent results can be achieved in this model. Even though unique solution is not achieved a finite number of solutions have been obtained from the proposed model.