An extension of the theory of elastic materials with voids to the case where the material undergoes an irreversible void growth is presented. The particularity of this theory is that the continuum is described by two kinematic variables: the displacements and the variation of the volume fi-action of material in the porous continuum. Motion is controlled by two governing equations, the classical one involving the displacement or stresses and another one that involves the other kinematic variable, similar to the governing equation in heat conduction problems. The degradation of the elastic moduli is described in the model by a damage scalar variable. A simplified model where the damage variable is proportional to the irreversible variation of volume fraction of material is discussed. From the governing equations, it is deduced that the equation which govems the growth of damage involves the second gradient of damage and a material parameter which plays the role of an internal length according to the analysis of strain localisation. The finite element implementation of the theory is briefly presented. The two variables are discretised separately and the form of the equations to be solved is similar to those obtained in coupled thermoelasticity. One dimensional finite element results of strain localisation show that a proper convergence upon mesh refinement is obtained. The equation which governs the irreversible variation of volume fraction (or the damage growth) acts as a localisation limiter.