A method is described for the solution of time‐dependent problems concerning the flow of viscous incompressible fluids in several space dimensions. The method is numerical, using a high‐speed computer for the solution of a finite‐difference approximation to the partial differential equations of motion. The application described here is to a study of the development of a vortex street behind a plate which has impulsively accelerated to constant speed in a channel of finite width; the Reynolds‐number range investigated was 15 ≤R≤ 6000. Particular attention was given to those features for which comparison could be made with experiments, namely, critical Reynolds number for vortex shedding, drag coefficient, Strouhal number, vortex configuration, and channel‐wall effects. The nature of the early stages of flow‐pattern development was also investigated.