The effect of a nearby plane boundary on vortex shedding from a circular cylinder is investigated for laminar flow. A two-dimensional finite difference numerical technique is used to solve the incompressible Navier-Stokes equations in primitive variable form on a computational mesh that is generated using a body-fitted coordinate transformation. Results are first presented for flows at Reynolds numbers of 80 and 100, based on the cylinder diameter, with the cylinder constrained against movement. Several cases of moving cylinder simulation are also presented for flow at a Reynolds number of 100. Fixed cylinder cases were run initially at both Reynolds numbers for an unbounded cylinder to confirm agreement of the simulation results with experimental evidence. The influence of a nearby plane boundary was investigated through a traverse of gap ratios beginning with a value of 3.0 and concluding with 0.5. Additional attention was focused on the behavior of the flow at gap ratios in the vicinity of the vortex shedding suppression gap ratio. Nearing the plate, a maximum Strouhal period was observed for each flow as suppression was approached. Features of the more viscous flow at the lower Reynolds number occurred at larger gap ratios than for the higher Reynolds number, as expected. The moving cylinder simulations were conducted primarily to demonstrate the capability of the simulator to accommodate the moving boundary of the cylinder. Initial gap ratios were chosen for examination based on the behavior of the fixed cylinder in the vicinity of the gap associated with vortex suppression.