A previous numerical study by Davis and Moore of vortex shedding from rectangles in infinite domains is extended to include the effects of confining walls. The major changes to the numerical modeling are the addition of a direct solver for the pressure equation and the use of an infinite-to-finite mapping downstream of the rectangle. The parameters in the problem are now Reynolds number, rectangle aspect ratio, blockage ratio, and upstream velocity profile. As each of these is varied, the effects upon the forces acting on the rectangle and the structure of the wake are discussed. Streakline plots composed of multishaped passive marker particles provide a clear visualization of the vortices. These plots are compared with smoke-wire photographs taken from a wind tunnel test. Strouhal numbers obtained both computationally and experimentally are compared for two values of the blockage ratio. Moving recirculation zones which appear between the wake and the walls are discussed.