The complexity of the physics of rock blasting is a longstanding modelling challenge. This work presents in detail a three-dimensional, material non-linear finite element based model for wave propagation, combined with a postprocessing procedure to determine the fracture intensity caused by blasting. The rock is described with the Johnson–Holmquist-2 constitutive model, an elastoplastic-damage model designed for brittle materials undergoing high strain rates and high pressures and fracturing; it is also combined with an instantaneous tensile failure model. Additionally, material heterogeneity is introduced into the model through variation of the material properties at the element level, ensuring jumps in strain. A detailed algorithm for the combined Johnson–Holmquist-2 and tensile failure model is presented and is demonstrated to be energy-conserving, and is complemented with an open-source MATLABTM implementation of the model. A range of sub-scale numerical experiments are performed to validate the modelling and postprocessing procedures, and a range of materials, explosive waves and geometries are considered to demonstrate the model’s predictive capability quantitatively and qualitatively for fracture intensity. Fracture intensities on 2D planes and 3D volumes are presented. The mesh dependence of the method is explored, demonstrating that mesh density changes maintain similar results and improve with increasing mesh quality. Damage patterns in simulations are self-organising, and form thin, planar, fracture-like structures that closely match the observed fractures in the experiments. The presented model is an advancement in realism for continuum modelling of blasts as it enables fully three-dimensional wave interaction, handles damage due to both compression and tension, and relies only on measurable material properties.