In this talk, we present and validate a computation framework based on the multiple scattering theory to model elastic metamaterials subjected to space-time modulation [1]. In more detail, we consider elastic waveguides equipped with time-modulated resonators. The proposed formulation allows to model an arbitrary distribution of resonators with distinct space-time modulation profiles and enables the computation of the related wavefield both within and outside the resonators' region. Moreover, the same framework can be applied to predict the dispersion relation of the modulated waveguide. To showcase the versatility of our approach, we discuss the dynamics of two representative space-time modulated systems, namely a beam and a half-space equipped with modulated resonators. Through these examples, we illustrate the advantages of the method over currently employed tools for studying elastic waves along space-time-modulated metamaterials, namely: i) the capability of modeling an arbitrary number of resonators without restrictions on their spatial configuration and modulation profile, (ii) the possibility of computing non-reciprocal wave propagation in higher-dimensional systems (2D and 3D), overcoming the limitations of existing analytical methods, such as the transfer matrix method, which is valid only for 1D wave propagation problems, (iii) the reduced computational costs compared to classical numerical schemes, as it eliminates the need for discretizing the entire system.