In this paper, we present a high performance computational electromechanical model of the heart, coupling between electrical activation and mechanical deformation and running efficiently in up to thousands of processors. The electrical potential propagation is modelled by FitzHugh-Nagumo or Fenton-Karma models, with fiber orientation. The mechanical deformation is treated using anisotropic hyper-elastic materials in a total Lagrangian formulation. Several material models are assessed, such as models based on biaxial tests on excised myocardium or orthotropic formulations. Coupling is treated using the Cross-Bridges model of Peterson. The scheme is implemented in Alya, which run simulations in parallel with almost linear scalability in a wide range computer sizes, up to thousands of processors. The computational model is assessed through several tests, including those to evaluate its parallel performance.