The two-dimensional flow past a circular cylinder is simulated numerically using a time-dependent finite difference Galerkin method. The temporal evolution of disturbances in the wake of a circular cylinder is examined for the supercritical Reynolds numbers of 55 and 80. After the symmetry condition is relaxed, antisymmetric disturbances emerge in the wake at a pure frequency and at a well-defined exponential growth rate. The predicted critical Reynolds number of 42 is in reasonable agreement with the experimentally determined value of 46. An important aspect of this work examines the stabilizing influence a second smaller cylinder has on the formation of vortex shedding behind the main cylinder. The placement of this second cylinder is shown to completely suppress vortex shedding at a Reynolds number of 55.