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The gantry cranes are currently one of the most common devices for transporting loads. They can be applied in many industry areas. This study focuses on the numerical analysis of only the portable gantry crane. Gantry cranes are widely applied to lift and transport smaller items around a working area in a factory or machine shop. The mathematical model and numerical simulations of mechanical phenomena in the gantry crane beam are presented in this paper. The problem was solved by the finite element method. Analysis was made to the gantry crane beam, which cross-section was the I-beam or T-beam. The numerical simulations are limited to strength analysis of the gantry crane beam which was load by the motion of the crane trolley along its length. As a result of the computations carried out, the stresses and displacements of the structure of gantry crane were obtained. The influence of changing the loading force position on generate the equivalent stress in the crane beam was evaluated. The research performed, which allows the evaluation of the stress state, pointing out the critical areas and values, were made in order to increase the strength of the structure of the gantry crane.