The overhead contact line (OCL) is the most effective way for supplying railway electric vehicles. The increase of the speed of vehicles increases power consumption and requires ensuring proper cooperation of pantographs with OCL. The paper describes the novel mathematical model of the OCL system and the simulation results. The primary objective is a more accurate analysis to increase the reliability of the evaluation of monitoring and diagnostics. The model was based on the Lagrange energy method. The paper presents the structure of the model and equations describing it, as well as the results of some laboratory tests that were performed to determine the model parameters. The selected results of simulations concerning the effects of force impact on the contact wire were carried out using the created model. The prepared program can be used for creating computer tools, which will support designers of OCL.