This paper is concerned with an efficient, variationally consistent, implementation for rateindependent dissipative solids at finite strain. More precisely, focus is on finite strain plasticity theory based on a multiplicative decomposition of the deformation gradient. Adopting the formalism of standard dissipative solids which allows to describe constitutive models by means of only two potentials being the Helmholtz energy and the yield function (or equivalently, a dissipation functional), finite strain plasticity is recast into an equivalent minimization problem. In contrast to previous models, the presented framework covers isotropic and kinematic hardening as well as isotropic and anisotropic elasticity and yield functions. Based on this approach a novel numerical implementation representing the main contribution of the paper is given. Analogously to the theoretical part, the algorithmic formulation is variationally consistent, i.e., all unknown variables follow naturally from minimizing the energy of the considered system. Extending previously published works on these methods, the advocated model does not rely on any material symmetry and therefore, it can be applied to a broad range of different plasticity theories. As an example, an anisotropic Hill-type model is developed. Numerical examples demonstrate the applicability and the performance of the proposed implementation.