A simple yet effective technique is used to obtain a numerical stability criteria for explicit time-marching algorithms in elastic-viscoplasticity. The resulting stability criteria are capable of accounting for non-associative and work hardening viscoplasticity for a wide variety of constitutive laws of the Perzyna-type. Conservative estimates for maximum permissible time step are obtained. This thesis investigates the level of conservativeness by considering different problems exhibiting various levels of constraint. Using the proposed stability criterion, assuming a linear flow function, non-hardening and uniform material properties, it is shown that the initial strain algorithm for plasticity and the initial strain viscoplastic algorithms are numerically the same. The intuitive approach used to obtain an estimate of maximum permissible time step was also used to develop an unconditionally stable implicit time marching scheme which avoids expensive matrix inversions. / Thesis / Master of Engineering (ME)