When designing new railway tracks or new buildings in the vicinity of existing railway lines, it is essential to conduct parametric studies to quantify the impact of design changes. Existing computational models demand substantial computational effort when predicting the full propagation path from track to building. Although computational complexity has been reduced by exploiting the geometrical invariance of the railway track, studies involving many design parameters are still hindered by the curse of dimensionality. By applying model order reduction techniques to predict railway induced vibration in buildings, a computational vademecum of the response is constructed, integrating soil and track parameters and facilitating fast parametric studies on vibration mitigation. The objective is to develop a model order reduction addressing the high-fidelity complex dynamic soil-structure interaction problem across a wide frequency range. To tackle this, Proper Generalized Decomposition (PGD) has been employed. The PGD formulation is based on the assumption of a separable form of the multi-dimensional field. Each contribution therefore consists of a rank-one tensor that is computed iteratively in a greedy manner. To this end, the PGD formalism is introduced into the weak form and the resulting non-linear problem is solved using fixed point iterations. Damping terms result in non-Hermitian properties of the operator, hindering convergence of the standard Galerkin PGD approach. Therefore, alternative solution strategies, like Petrov-Galerkin based solvers, are considered. We compare the classical greedy rank one update with a greedy Tucker approximation method. The PGD formulation is first elaborated for a simplified model consisting of an Euler-Bernoulli beam on a Winkler foundation, which is solved in the wavenumber-frequency domain. Foundation properties are added as extra coordinates to illustrate the use of PGD for a parametric problem. This PGD formulation is subsequently extended for the case of ballasted track on a heterogenous soil medium, modelled with finite elements in combination with complex frequency-shifted perfectly matched layers (CFS-PML). Model parameters now also include the ballast and soil properties. The considered algorithms are compared in terms of convergence, memory requirements, and CPU time.