Ballistic gelatine is a surrogate to muscle tissue, often used in experiments to study the effects of bullet-tissue interaction. To enable the dynamic computational modelling of ballistic gelatine and the bullet-gelatine interaction in particular, a necessary mechanical framework is established. A hyper-visco-elastic model is presented in detail, including a damage function based on a non-linear strain failure surface theory and an equation of state (EOS) suitable for high-velocity impact and shock waves. The continuum mechanical framework includes the derivation of the stress and elasticity tensors in both the Lagrangian and the Eulerian descriptions. To facilitate the incompressible behaviour of gelatine and maintaining numerical stability, the framework is based on a nearly incompressible theory by using a multiplicative decomposition of the deformation gradient into a volumetric and an isochoric part. To model ballistic gelatine, a suitable isotropic strain-energy function is suggested. The formulation of the framework, however, enables easy manipulation to future alternative strain-energy functions by explicitly stating the few constitutive parameters that needs changing. The framework and model is implemented as a custom built user defined model in the commercial hydrocode software LS-DYNA. Two numerical examples are shown. In the first, a steel sphere impacts a block of gelatine. The steel sphere impacts the gelatine at 1000 m/s, a speed that no hyperelastic model available in the standard material library of LS-DYNA could handle satisfactorily. Even though non-realistic material parameters are used for the gelatine model, visual comparison of the numerical results indicate a fairly good match with experimental data. In the second example, a cylindrical bullet impacts a block of gelatine at the same speed but at two different angle of attack, 0º and 2º. With 0º angle of attack, the bullet passes straight through the block without tumbling. Using 2º angle of attack, however, results in severe tumbling of the bullet as it passes through the gelatine block. The tumbling is in accordance to experimental observations.