Heterogeneous materials present a mechanical response strongly dependent on the static and kinematic phenomena occurring in the constituents and at their joints. At the mesoscopic level the interaction between the units is simulated by mean of apposite mechanical devices such as the zero thickness interface model where contact tractions and displacement discontinuities are the primary static and kinematic variables respectively. In heterogeneous materials the response also depends on joint internal stresses. The introduction of internal stresses brings to the interphase model or an enhancement of the classical zero-thickness interface. With the term 'interphase' we shall mean a layer separated by two physical interfaces from the bulk material or a multilayer structure with varying properties and several interfaces. Different failure conditions can be introduced for the physical interfaces and for the joint material. The interphase model has been implemented in an open-source research-oriented finite element analysis program for 2D applications. © 2013 Taylor & Francis Group, London, UK.