The sedimentation of solid spherical particles arranged in a regular periodic lattice is investigated for finite Reynolds number flows with particle volume fractions less than 20\%. We have performed numerical simulations using a spectral/element method to solve the unsteady Navier-Stokes equations on a well resolved mesh for particle Reynolds numbers up to 63. The lattice structure of the particle array is represented by periodic boundary conditions on a unit cell. A third order Adams-Bashforth scheme is used to advance the flow field in time. The flow evolves to a steady state driven by a uniform pressure gradient. Our results show that for moderately low concentrations the fluid velocity is high and particle interactions are dominated by wake effects as they settle under gravity. As the concentration increases, the close proximity of the particles to one another inhibits the normal development of the wake structure as the fluid velocity is slowed. Further investigation at higher Reynolds numbers provide an opportunity to examine the transition to unsteady flow. Extending the model in this way enables the effects of the periodic geometry on the flow structure to be observed and may provide some insight into the flow stability.