AbstractThis paper addresses fluid‐driven crack propagation in a porous medium. Cohesive interface elements are employed to model the behaviour of the crack. To simulate hydraulic fracturing, a fluid pressure degree of freedom is introduced inside the crack, separate from the fluid degrees of freedom in the bulk. Powell‐Sabin B‐splines, which are based on triangles, are employed to describe the geometry of the domain and to interpolate the field variables: displacements and interstitial fluid pressure. Due to their ‐continuity, the stress and pressure gradient are smooth throughout the whole domain, enabling a direct assessment of the fracture criterion at the crack tip and ensuring local mass conservation. Due to the use of triangles, crack insertion and remeshing are straightforward and can be done directly in the physical domain. During remeshing a mapping of the state vector (displacement and interstitial fluid pressure) is required. For this, a new methodology is exploited based on a least‐square fit with the energy balance and mass conservation as constraints. The accuracy to model free crack propagation is demonstrated by two numerical examples, including crack propagation in a plate with two notches.