Simultaneous steady forced and free convective flow past a heated or cooled body in a semi-infinite porous medium subject to the Darcy–Boussinesq approximation is treated analytically and numerically. A correction term is derived in terms of the Rayleigh (Ra) and Péclet (Pe) numbers for the velocity and temperature fields far from the body; this is subsequently implemented in a numerical treatment, using finite-difference techniques in elliptical coordinates, for 1[les ]Pe[les ]100 and [mid ]Ra[mid ][les ]103. Flow separation is observed for both heating and cooling, perhaps surprisingly so for the former case since the flow near the plate is being accelerated by comparison with the forced convection case. A simple analogy with inviscid flow theory serves to illustrate the manner in which separation eddies are formed for both heating and cooling cases.