High precision and productivity of robotic manipulators are actually requirements involved by the necessity to obtain greater general performances of industrial robots. The higher speeds and accuracy are greatly influenced by the elasticity of general mechanical structure of industrial robot. According to these assumptions this paper presents, in its first part, a general mathematical model, made for gantry robots, for determining the positioning error, valid for a real robot structure, based on the mathematical Denavit–Hartemberg model, to witch, adding matrix expressions that are describing the errors of kinematic joints. a and the mathematical background for determining the loads on its P–joints. Also a real gantry robot is presented; a gantry robot model from Güdel product range, for this one, the second part of the paper describes the distribution of loads on kinematic couplings, the aim being to evaluate the influence of elastic displacements of joints elements on gantry robot volumetric accuracy.