This work surveys a broad range of related issues in quasistatic elastoplasticity, beginning with a development of an internal variable constitutive theory. The initial-boundary value problem is then considered, and the remainder of the work is concerned with the properties of the time-discrete problem. It is shown how this discrete problem has associated with it a holonomic constitutive law (that is, one relating stress to strain or strain increment), and this holonomic law in turn forms the basis of a solution algorithm. Conditions for the convergence of the algorithm are discussed. The entire treatment applies to the spatially continuous problem.