Summary: We implement the spatially periodic boundary conditions in finite element solutions of the Navier-Stokes equations based on the streamfunction-vorticity formulation. Periodic boundary conditions are enforced at both inflow/outflow and lower/upper boundaries. As an example of application, we consider the fluid flow, at two different Reynolds numbers, through an array of pin fins. The limiting assumption of symmetry conditions at the boundaries parallel to the main flow is shown to yield unphysical-looking configurations.