Fluid flow in a partially porous square cavity with the top wall moving in its own plane is studied for different Darcy numbers, porous fractions, and orientations of the porous–clear interface at a fixed Reynolds number (Re=103) and porosity (ϕ=0.7). Darcy number (Da) and porous fraction (η) are varied in the range 10−5 to 10−1 and 0 to 1, respectively. For a given porous fraction, three arrangements of porous material resulting in an interface oriented at an angle of (a) 0°(parallel to the moving wall); (b) 45°(inclined towards the moving wall); and (c) −45°(inclined away from the moving wall) are considered. In this study, the effect of these parameters on the vortex structure as well as quantities such as |Ψ|c and |ω|c (the absolute value of stream function and vorticity at the center of primary vortex) and |ω|w, min (the minimum absolute vorticity on the moving wall) are examined. Based on the one-domain approach, the generalized porous flow model, which treats the properties of the medium as variable parameters, is employed to describe the flow behavior in the cavity. The governing equations are solved by the second-order projection method on a quadtree grid. The numerical results show that, as the Darcy number decreases, the flow pattern changes in accordance with the reduced inertial effect. Also, as indicated by |Ψ|c, the flow rate in the cavity decreases regardless of the interface orientation. However, there exists a critical Da below which the primary vortex takes a complex shape and an increase in the volume flow rate is observed. Unlike the Darcy number, the porous fraction has a monotonic impact on the flow rate. Nevertheless, |ω|c as well as |ω|w, min show non-monotonic variation with the Darcy number and porous fraction. In addition, with respect to the parallel interface, a small and a large deviation in the physical quantities are noted for the oblique interface with angle 45° and −45°, respectively. Also, at a given Da, the change in interface angle has a different effect on the flow quantities in the low and high Darcy number regimes. Furthermore, the flow characteristics are seen to be approaching their constant state as Da→0. The flow features in the clear region of the parallel interface cavity, obtained at low Darcy number, are found to be very close to the literature data for a clear cavity with identical size. Thus, one can conclude that the present observations made for low Darcy numbers can also be applied to the clear cavity with geometry and dimensions identical to the clear region of the partially porous cavity.