In this paper, unstable fracture propagation obtained in a in-house performed experimental Wedge Splitting Test (WST) is simulated by means of the FEM and fracturebased zero-thickness interface elements. In order to obtain a specimen geometry suitable for a stable WST without modifying the remaining significant parameters of the test (machine stiffness and control parameter), additional simulations were performed varying the length of the specimen notch, until a load-COD (Crack Opening Displacement) curve without snap-back was obtained. Finally, a new experimental WST with the modified geometry was carried out leading to a stable load-COD curve. In the simulations, elastic continuum elements were used to represent the rock, the steel loading plates and the testing machine compliance via an “equivalent spring”, whereas interface elements were used for the notch and along the potential crack path. The interface elements representing the notch were equipped with linear elastic constitutive law, with very low elastic stiffness Kn and Kt so that they do not oppose any significant resistance to opening. For the interface elements along the fracture path, an elastoplastic constitutive model with fracture energy-based evolution laws was used.