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The article explores the modeling of the interaction between the pantograph and the catenary, which is a relevant task in the development and optimization of current collection systems. The subject of the article is the modeling of the catenary, with finite element models and lumped parameter models being the most widely used approaches. Their key characteristics are highlighted: finite element models offer high accuracy but require significant computational resources, whereas lumped parameter models allow for a quicker assessment of interactions but have limitations due to their simplified representation of physical processes. The aim of this study is to improve the accuracy of modeling the interaction between pantographs and the catenary using lumped parameter models. As part of the research, an improved catenary model is proposed, in which the lumped mass is replaced with an inerter. This modification eliminates the issue of forced oscillations and enhances the accuracy of system dynamics modeling. The proposed model is implemented in MATLAB Simulink, and its validity is confirmed through correlation analysis, demonstrating better agreement between the calculated and experimental data compared to existing models. The obtained results show that the proposed approach allows for a more accurate simulation of the interaction between the pantograph and the catenary, making it a promising solution for use in the design and optimization of current collection systems in railway transport.