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This research is inspired by mathematical modelling of railcar dynamics and deals with developing a methodology for estimating the impact loads acting on freight cars using measured acceleration data in order to determine their limiting magnitudes for the alarm generation. The developed scheme consists of the following steps. First, artificial neural network technology (ANN) is adapted to predict longitudinal forces in freight cars. Impact tests data for accelerations and forces were used for training ANN. The issue related to the lack of experimental results for training the network is addressed. A possibility of alternative theoretical training using mathematical models is studied. A restricted scope of conventional mathematical models based on rigid body dynamics is discovered. In particular, these models ignore the effect of self-equilibrated loads and internal dissipation. Next, an advanced perturbation model is derived, taking into account low frequency internal motion with inhomogeneous stiffness, density, and viscosity incorporated. The developed advanced model is applied to the evaluation of impact forces arising at coupled impact. The aforementioned model follows from a low-frequency analysis of a viscoelastic inhomogeneous bar, subject to end loads. The longitudinal variation of the problem 2 parameters is taken into consideration. Explicit asymptotic corrections to the conventional equations of rigid body motion are derived in an integro-differential form. The refined equations incorporate the effect of an internal viscoelastic microstructure on the overall dynamic response. Comparison with the exact time-harmonic solutions for extension and bending of a bar demonstrates the efficiency of the developed approach.