Discontinuities have an important influence on the bulk behaviour of geomaterials. Discontinuities can be physical openings like fractures and joints, interfaces between different material types, or zones with different material behaviour like mortar or reinforcement material. Bulk material behaviour is often determined by the behaviour of the discontinuities by providing preferential pathways for flow or by acting as failure planes. FEM simulations with continuum elements are typically not suitable for modelling discontinuities with no width, due to the inability to model discontinuous fields. One solution is to represent discontinuities using zero-thickness interface elements. Inserting zero-thickness interface elements allows for discretely modelling discontinuous behaviour between neighbouring continuum elements. The continuum elements are then used to represent the bulk behaviour and the zero-thickness interface elements discretely model the discontinuity. A new constitutive law for zero-thickness interface elements that expands the cohesive zone model with friction is formulated in this thesis. The tangential stress response of the interface elements consists of a cohesive and frictional contribution. The cohesive component of the constitutive law is based on the Crisfield’s cohesive elasto-damage model, which is characterised by a linear elastic response to increased relative displacement, followed by degradation of the cohesive strength and stiffness. The elasto-plastic frictional component is based on the Dahl friction model and implemented in parallel to the cohesive component. The implemented new constitutive law is verified in a large variety of loading conditions, including tangential loading, tangential loading with a reversion of loading direction and combinations of mixed-mode loading. The constitutive laws are validated based on shear box experiments performed on London clay where interface elements are used to model a predefined shearing plane. The cohesive and frictional constitutive law can represent confinement-dependent tangential stress and residual stress at large relative displacements. These features, observed in the shear box experiments, could not be reproduced by the purely cohesive constitutive law. This new constitutive law can be used to better model discontinuities in geomaterials represented by zero-thickness interface elements.