The moving load problem is an important issue that affects many engineering fields and causes dynamic effects in the cranes. Nowadays, as the cranes are operated with higher speeds, in the design of the cranes, the dynamic behaviors arising from the moving loads should be investigated and analysed accurately. Therefore, dynamic behaviors of the crane beams under the moving load were investigated in this study. For that purpose, the moving load problem was mathematically stated for a simply supported, homogeneous, an isotropic Euler-Bernoulli type beam representing the main beam of the crane. The moving load is acted as a concentrated, singular load on the beam and the crane beam was obtained as damped, not undamped unlike the previous studies. Thus, from the solution of these mathematical expressions, the mathematical models which gives the deflections, bending moment, shear forces were obtained for the crane beams. Then, the algorithms were created in the Matlab program and the simulation studies were carried out for various working scenarios. The scenarios were determined for different speeds and different mass ratios and every scenario was evaluated by the diagrams and tables the deflections, bending moment, shear force that occurred on the beam in the damped situation. Besides, the results were also compared with the static situation. As a result, the studies show that static calculations are inadequate for cranes working in high speed. So, it will be appropriate both to analyze dynamic behaviors arising from the moving load according to the working scenarios and to design according to obtained results for the cranes.