Understanding the physics of the rupture process requires very sophisticated and accurate tools in which both the geometry of the fault surface and realistic frictional behaviours could interact during rupture propagation. New formulations have been recently proposed for modelling the dynamic shear rupture of non-planar faults (Ando et al., 2004; Cruz-Atienza &Virieux, 2004; Huang &Costanzo, 2004) providing highly accurate field estimates nearby the crack edges at the expanse of a simple medium description or high computational cost. We propose a new method based on the finite volume formulation to model the dynamic rupture propagation of non-planar faults. After proper transformations of the velocity-stress elastodynamic system of partial differential equations following an explicit conservative law, we construct an unstructured time-domain numerical formulation of the crack problem. As a result, arbitrary non-planar faults can be explicitly represented without extra computational cost. The analysis of the total discrete energy through the fault surface leads us to the specification of dynamic rupture boundary conditions which insure the correct discrete energy time variation and, therefore, the system stability. These boundary conditions are set on stress fluxes and not on stress values, which makes the fracture to have no thickness. Different shapes of cracks are analysed. We present an example of a bidimensional non-planar spontaneous fault growth in heterogeneous media as well as preliminary results of a highly efficient extension to the three dimensional rupture model based on the standard MPI.