Purpose: To analyse and identify the limitations associated with the use of existing catenary suspension technologies and calculation methods in modern conditions. Methodology: A mathematical model for calculating a semi-compensated overhead suspension was developed. This model was based on the finite element method (hereinafter referred to as FEM), and its implementation was carried out in the ANSYS Workbench software package. To confirm the effectiveness of the developed model, the calculation results obtained using this FEM model were compared with the results obtained using the existing methodology. This enabled a thorough evaluation of the pros and cons of each method, highlighting the rationale behind transitioning to more contemporary and precise calculation techniques. Results: The analysis has revealed that the current calculation methods for catenary suspension do not accurately reflect real conditions, potentially leading to issues in design and operation. The research has demonstrated the need to improve the existing methods and adapt them to realities, with an emphasis on the introduction of modern approaches, such as mathematical modelling, which will significantly increase the accuracy and reliability of calculations. Practical significance: The disparities in the calculations emphasise the necessity to employ contemporary methodologies for determining the parameters of the catenary system, particularly in challenging circumstances. The finite element method is a highly versatile modelling technique. It can be used in models that will consider a range of factors impacting the operation of the catenary system, such as current, heating temperature and changes in wire tension. Design specialists can effectively utilise such models, including when transitioning to BIM technology and engaging in scientific activities.