Abstract The present study investigates the modelling capabilities offered by the multi-surface damage-plasticity FE-formulation illustrated in Part I [1] when integrated with a regularized extended finite element model. The aim is to tackle discontinuous displacements and interfaces. In particular, we show how to embed a regularized discontinuity within an element, carry out the transition from the continuous to the regularized discontinuous regime and obtain physically consistent results. We present a wide set of applications ranging from brittle to ductile failure, displaying the effectiveness of the proposed FE-approach versus the experimental results.