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This paper includes an analysis of the mechanical phenomena in the gantry crane beam, because the gantries are currently one of the most common devices for the transporting loads. The design of modern mechanical constructions is a complex task that requires use of appropriate tools. Such a modern tool is numerical simulation which uses the various numerical methods. One of the best known methods is the finite element method, also used here. 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. Analysis was made to the gantry crane beam which cross-section was an I-beam and ends were fixed in different ways. As a result of the computations carried out, the stresses and displacements of the structure of gantry were obtained. The influence of changing the loading force position and the restraints type on generate the equivalent stress in the gantry crane beam was evaluated. It sought to that the maximum value of Huber-Mises stress induced in the gantry crane beam was less than the strength of material, because then the design is safe