Fluid flow and heat transfer in two-dimensional finned passages were analyzed for constant property laminar flow. The passage is formed by two parallel plates to which fins are attached in a staggered fashion. Both the plates are maintained at a constant temperature. Streamwise periodic variation of the cross-sectional area causes the flow and temperature fields to repeat periodically after a certain developing length. Computations were performed for different values of the Reynolds number, the Prandtl number, geometric parameters, and the fin-conductance parameter. The fins were found to cause the flow to deflect significantly and impinge upon the opposite wall so as to increase the heat transfer significantly. However, the associated increase in pressure drop was an order of magnitude higher than the increase in heat transfer. Streamline patterns and local heat transfer results are presented in addition to the overall results.