This paper presents nonlinear mixed formulations to simulate the material failure process in solids by its finite element approximation. The formulations presented are the corresponding virtual work by the virtual stresses and displacements and the virtual work by displacements and strains. Both formulations presented are derived from the principle of virtual work with four independent variables. The beha- viour of the material is governed by an isotropic continuum damage model equipped with two internal variables at each integration point. In the numerical implementation, the displacement-stress formulation presents numerical problems when the behaviour of the material approaches complete damage, thus only the displacement-strain formulation was implemented. The advantage of the strain-displacement over a typical displacement formulation to simulate the material failure process with damage models as strain concentrations is discussed. To show the validity and illustrate the effectiveness of the displacement-strain formulation, results from some representative numerical examples are presented and discussed within the framework of continuum approximations.