Realistic simulations of earth processes such as faulting, shearing, magma flow, subduction and convection often require the consideration of non-Newtonian Effects such as elasticity and power law creep. As the deformations involved in geological deformation are often large the constitutive relationships must maintain certain geometric terms to ensure that the tensor properties of the model are conserved. A model with such properties is termed as objective. There are a wide range of objective, visco-elasto-plastic models to choose from. The main structural difference between these models consists in the choice of the objective stress rate, e.g. Jaumann, Oldroyd, Truesdell - rates (see Kolymbas and Herle, 2003, for a recent discussion). In this paper we give an outline of a thermo-visco-elastic-plastic model including a discussion of numerical aspects such as the derivation of a consistent incremental form. The viscous part of the deformation involves a combination of both Newtonian and power law creep. Plastic deformations are described by means of a standard Prandtl-Reuss flow rule combined with a von Mises yield criterion. In planetary scale flow modeling the yield criterion is required as a stress limiter during episodic events e.g. in connection with the initiation of subduction. The temperature sensitivity of the viscous deformation is considered by means of an Arrhenius relation involving a pressure dependent reference (melting) temperature. The salient features of the model are first explored by means of analytical and numerical solutions of a simple shear problem for an infinite strip with fixed and prescribed shear velocities on the bottom and top of the layer respectively
