The present study was conducted to numerically investigate the transport mechanism of laminar combined convection in a shear- and buoyancy-driven cavity. The focus was on the interaction, of the forced convection induced by the moving wall with the natural convection induced by the buoyancy. Two orientations of thermal boundary conditions at the cavity walls are considered in order to simulate the aiding and opposing buoyancy mechanisms. Velocity and temperature distributions of the fl;ow are carried out through a stream function-vorticity transformation with a finite difference scheme. Parametric studies of the effect of the mixed convection parameter, Gr/Re-2, on the fluid flow and heat transfer have been performed. Calculations cover Re=100, Pr=0.71 and Gr/Re-2 the range of 0.01-100. Three different regimes are observed with increasing Gr/Re-2: Forced convection (with negligible natural convection), mixed convection (comparable forced and natural convection) and natural convection (with negligible forced convection). The code developed was carefully tested for the two limiting cases, the pure forced convection and the pure natural convection, for which experimental and numerical data are available. (C) 1999 Elsevier Science Ltd.