Bridge cranes carrying structure is one of their essential elements. The most popular, solid-walled metal sheet structures have higher mass that leads to a stable trend in metal reduction. Due to the wide range of loadings, mass reduction calculations are faced with various problems that could be solved effectively by an appropriate methodology, as the one proposed here. The underlying techniques in the methodology are 3-D computer models and mathematical methods such as FEM, the matrix exponential, Newmark, Kutta-Merson, FFT, etc. realized by ANSYS, MATLAB, visualNastran, SolidWorks. The carrying structure dynamic response has been studied when operating are the mechanisms for: hoisting, by using models with distributed and discrete parameters; travel, during steady and transient processes, by models that account for the runway obstacles. There have also been developed full 3-D models, that accounting for contacts, welds, etc, produce stress, fatigue, etc. results used to detect critical structure points out of reach in real experiments. The proposed methodology could be of use to post- graduates, scholars and crane structure designers.