Unlike the broadly studied influence of the in-plane magnetic fields on magnetic domain structures in thin-film elements, not much is known to date, on the changes of the domain structure driven by external magnetic fields applied perpendicular to the plane. Using high-resolution transmission electron microscopy studies combined with micromagnetic modeling, we investigated the effect of static, strong perpendicular fields on square and disk-shaped mesoscopic permalloy elements with a vortex flux-closure magnetization structure. In the case of square elements, we discovered an unexpected, pronounced, and reversible bending of the 90° domain walls, which increases with the field strength and changes direction when the field direction is reversed. By means of micromagnetic simulations and atomic force microscopy studies, we demonstrate that this effect is connected with the minute curvatures of the sample surface. The slight curvature arises from surface tensions in the membrane on which the microstructures are fabricated.