Polyurethane (PU) foam can display mechanical anisotropy because of elongation of cells in the vertical direction when component liquid chemicals are mixed to generate PU foam. Existing studies on the anisotropic mechanical response of PU foam appear limited, particularly for high strain-rate loading. In this investigation, a PU foam with an apparent density of 36.5 kg/m3 was fabricated, and 40 mm cubic specimens were cut at 0°, 30°, 45°, 60° and 90° to the foam-rise direction, and subjected to quasi-static (0.0042–0.42 s−1 global strain rate) and dynamic (∼190 s−1 global strain rate) compression, to identify the effects of loading direction and strain rate on the resulting mechanical response. Dynamic compression tests were performed using a modified Hopkinson bar device, with force equilibrium in the foam specimens examined and validated via finite element modelling. The overall stress–strain response, as well as the deformation modes, varies significantly with loading direction. For compression along the foam-rise direction (0°), deformation of foam cells is dominated by unstable buckling of cell struts; this leads to deformation localization and subsequent layer-by-layer crushing. The corresponding overall stress–strain response displays a brief post-yield strain softening phase, generated by the initiation and development of localized deformation in the first cell layer to collapse. This is followed by a protracted stress plateau, whereby localized crushing propagates layer-by-layer through the specimen. For compression along the transverse direction (90°), deformation of foam cells is characterized by stable bending of cell struts, leading to uniform deformation within the foam specimen, accompanied by gradual post-yield hardening in the overall stress–strain response. For compression at various inclinations (e.g. 30°, 45°, 60°) to the foam-rise direction, foam cells deform via a combination of buckling and bending of cell struts, and the overall stress–strain response lies between that corresponding to compression along the foam-rise and the transverse directions. With respect to the influence of strain rate, a higher deformation rate generates a stiffer and stronger overall stress–strain response. Several material parameters — i.e. overall elastic stiffness, yield stress, densification strain and effective energy absorption capacity — were examined to characterize the mechanical properties of PU foam. The elastic stiffness, yield stress and effective energy absorption capacity all decrease with an increase in loading angle to the foam-rise direction, but they increase with strain rate. However, the densification strain varies little with loading angle or strain rate.