A wedge-shaped failure mechanism occurs when a composite ply in a laminate is loaded under transverse compression. Because of this, a typical failure model for tensile load cases is not straightforward applicable for compressive load cases. In this paper, a method is described to approximate the compressive behavior using a vertical crack plane. Rather than adopting the crack topology, a transformation is applied prior to the evaluation of the cohesive law. The method is applied on predefined interface elements in a 2D model, as well as on cohesive segments in the extended finite element method in a 3D model. It is found that the compressive failure of composite laminates including the wedge effect can be approximated accurately with this method using a vertical crack plane. In 3D, a variable fracture plane angle is easily taken into account with the method, which means that the whole range of failure modes, from tensile, through shear-dominated to compressive failure can be covered in a single approach.