The stress analysis of a hook crane submitted to some vertical static force is a simple FEM problem, approached here using SolidWorks Simulation software. Our purpose was to simulate different possibilities to slightly modify the shape of the hook crane, without adding too much material, in order to reduce the maximum stress induced in the hook. The shape design concerned here both the shape of the (transversal) cross-section and the shape of the hook longitudinal profile. The stress distribution is strongly depending on the shape of the hook crane, but it is almost independent on the hook material, since the bending mechanical stress, which is dominant in this combined bending and elongation case study, is not depending on the elastic modulus of the hook material. Obviously, the material choice is crucial from the point of view of the yield strength, usually hardened steels with increased yield strength are preferred. In what concerns the shape design improvement from the point of view of the cross-section (of equal area), our study confirmed that the trapezoidal section proposed generally in the literature corresponds to a reduced maximum induced stress. As a new result, a T-shape hook crane cross-section seems to prove better results that the trapezoidal section. To avoid stress concentrators, a combination between the trapezoidal and T-shape cross-sections has been also considered. The idea is to avoid as much as possible the discontinuity points on the outer contour of hook cross-section, since these discontinuity points are usually mechanical stress concentrators. A shape design improvement has been performed also in what concerns the longitudinal section/profile of the hook crane.