Abstract The equilibrium scour depth at uniform single bridge piers depends on a large number of variables, including the pier horizontal cross-section shape and its alignment angle towards the flow direction. The influence of these variables has been studied by only a few researchers, mostly, on the basis of tests that were far from approaching equilibrium. This experimental study aims at revisiting the influence of piers׳ shape and alignment on local scouring for length–width ratios smaller than or equal to 4, by increasing the experimental evidence. Fifty five long-duration laboratory tests were run under steady, clear-water flow, close to the threshold for initiation of sediment motion. Five pier shapes were considered: circular, rectangular square-nosed, rectangular round-nosed, oblong, and zero-spacing (packed) pile-groups; the tested skew-angles were 0°, 30°, 45°, 60°, and 90°. It was concluded that i) the shape factor can be taken as 1.0, for rectangular round-nosed and oblong cross-section piers, and as 1.2, for rectangular square-nosed and packed pile-group cross-section piers, ii) the shape factor does not vary significantly with the duration of tests, this way confirming the robustness of the shape factors reported to date, iii) the effect of shape is present at skewed piers although the associated coefficients remain in the narrow range of 1.0–1.2, and iv) for length–width ratios smaller than 4, the shape factor is of the same order of magnitude as the skew angle factor and should not be neglected.