A formulation and algorithmic treatment of static and dynamic plasticity at finite strains based on the multiplicative decomposition is presented which inherits all the features of the classical models of infinitesimal plasticity. The key computational implication is this: the closest-point-projection algorithm of any classical simple-surface or multi-surface model of infinitesimal plasticity carries over to the present finite deformation context without modification. In particular, the algorithmic elastoplastic tangent moduli of the infinitesimal theory remain unchanged. For the static problem, the proposed class of algorithms preserve exactly plastic volume changes if the yield criterion is pressure insensitive. For the dynamic problem, a class of time-stepping algorithms is presented which inherits exactly the conservation laws of total linear and angular momentum. The actual performance of the methodology is illustrated in a number of representative large scale static and dynamic simulations.