In the context of the developing of a numerically efficient model of railway induced ground vibrations, the problem of an infinite, longitudinally-varying and harmonic strip load acting on the surface of a viscoelastic half-space is reformulated in order to improve its numerical evaluation. On one hand, the static integrands of this specific problem are modified and introduced into the original integrands to reduce their spectral content at high wavenumbers, saving computational time needed for the numerical integration. On the other hand, a change of variable is applied on the displacements integral solutions resulting on frequency independent integrands. These formulae allow to obtain the displacement solution in the complete x-y-ω field easier and, mostly, faster