A study of hypersonic viscous interaction on a flat plate is presented. It is shown that the numerical solutions develop singular behavior with respect to the initial data employed. Nonsingular solutions are possible only when a parameter in the initial data is fixed at some specific value which is not knowna priori. The origin of this singular dependence is then investigated. It is found that the problem is improperly set as an initial value problem because the interaction dynamics contain upstream influence. If the problem is attacked as an initial value problem, then a constraint must be placed on the initial flow profiles if a bounded solution is to result. Finally, an approximate numerical method is presented to develop this nonsingular solution for the original system of coupled nonlinear equations.