Suitable material models have to be chosen to achieve realistic numerical simulations of the mechanical behavior of components and structures as well as a reliable identification of material parameters for finite deformations analyzing inhomogeneous displacement fields. The fundamental relations of the kinematics of an elasto-plastic continuum are formulated using the multiplicative split of the deformation gradient, the concept of dual variables and the covariance principle. A thermodynamically consistent system of differential and algebraic equations (DAE) is derived in the reference configuration to describe the rate-independent inelastic material behavior. It contains the associated flow rule, evolutional equations for the internal variables describing different kinds of hardening and the yield condition. An algorithm for the solution of the DAE based on a suitable time discretization of the differential equations is presented as well as a numerical example using the experimental FE-code PMHP on parallel computers developed at the Chemnitz University of Technology. An important advantage of the presented algorithm is its high efficiency in case of the determination of the consistent material matrix as well as within the scope of the semianalytical sensitivity analysis as a deciding part of the parameter optimization process.