A Green function approach is utilized to investigate wave interaction with a rectangular pit of finite dimensions in water of otherwise constant depth. The fluid domain is divided into two regions: an interior region which is finite in extent and represents the pit itself, and an exterior region consisting of the remainder of the fluid domain. An integral equation solution utilizing an appropriate Green function in the exterior region is linked to an interior solution in the form of a Fourier expansion containing unknown potential coefficients through matching conditions at the imaginary interface between the two regions. Discretizing the integral equation leads to a matrix system for these potential coefficients which may be solved using standard matrix techniques. Numerical results are presented for several example geometries which illustrate the effect of pit characteristics and incident wave direction on the water surface elevation.