Development and verification of a mathematical model for calculating the additional dynamic impact force exerted by railway vehicle wheels with isolated irregularities, such as wheel flats or sliders, on the railway track, is presented. Additionally, a simplified engineering method for practical application has been created. Methods: The research utilizes the analytical solution by A. Ya. Kogan, which describes the dynamics of the defective wheel – rail interaction. Numerical modelling was conducted using the Wolfram Mathematica environment. The model underwent verification through a comparison with the experimental data gathered from strain gauge circuits positioned on the rail web. A three-parameter regression analysis was employed to establish the engineering methodology. Results: A mathematical model has been developed and verified, accurately capturing the physical essence of the process, with discrepancies from experimental data typically not exceeding 10%. The analysis has revealed the nature of the influence of key parameters, namely the force significantly increases (by a factor of 2–5) with deeper irregularities; the relationship with speed is non-monotonic peaking at 40–50 km/h; and an increase in the track elastic modulus enhances the force amplitude while accelerating its decay. A simplified regression dependence for engineering calculations has been proposed, demonstrating a high accuracy (R² = 0.995) for irregularity depths exceeding 0.6 mm. Practical significance: The practical implications of this research establish a scientific and methodological framework for evaluating impact forces resulting from rolling stock wheel defects. The proposed model and engineering methodology can be employed for diagnosing track conditions, predicting vibration impacts, and designing to ensure the durability of railway infrastructure and the safety of operations.