We propose a dynamics framework for representing progressive localized failure in materials under quasi-static loads. The proposed model exhibits no mesh dependency, since localization phenomena are taken into account by using the embedded strong discontinuities approach. Robust numerical tool for simulation of discontinuities, in which the displacement field is enhanced to capture the discontinu-ity, is combined with continuum damage representation of FPZ-fracture process zone. Based upon this approach, a two-dimensional finite element model was developed, capable of describing both the diffuse damage mechanism accompanied by initial strain hardening and subsequent softening response of the structure. The results of several numerical simulations, performed on classical mechanical tests under slowly increasing loads such as Brazilian test or three-point bending test were analyzed. The proposed dynamics framework is shown to increase computational robustness. It was found that the final direction of macro-cracks is predicted quite well and that influence of inertia effects on the obtained solutions is fairly modest especially in comparison among different meshes.