Natural convective heat transfer across a rectangular enclosure containing air whose bottom surface is heated and whose top surface is cooled and whose side surfaces are adiabatic has been considered. In some situations involving such enclosures, the top and bottom enclosure surfaces are inclined at a relatively small angle to the horizontal. The purpose of the present study was to numerically determine the effect of such inclinations of the upper and the lower surfaces on the heat transfer rate across the enclosure. In this study the case where the top surface of the enclosure is inclined upward and the bottom surface is inclined downward, both inclinations being at the same angle to the horizontal, and where the two side surfaces are vertical has been considered. In undertaking the study, it has been assumed that the flow in the enclosure is steady, two-dimensional, and laminar. It has also been assumed that the air properties are constant except for the density change with temperature, i.e., the Boussinesq approach has been adopted. Enclosures with aspect ratios of 2, 4 and 6 and with surface angles of inclination of between 0° and 8° have been considered. The numerical solution has been obtained using the commercial solver ANSYS FLUENT^©.