A three-dimensional multi-scale discrete–continuum model (Finite Volume Method × Discrete Element Method, FVM × DEM) is developed for a discrete-based description of the mechanical behavior of granular soils in boundary value problems (BVPs). In such a scheme, the constitutive response of the material is derived through direct DEM computations on a representative volume element attached to each mesh element. The developed multi-scale approach includes the inertial effect in the stress homogenization formulation and serves to study the mechanism of propagation of seismic waves, in comparison with a more classical BVP simulation that adopts an advanced bounding surface plasticity model ‘‘P2PSand’’. We start with a detailed and fair calibration and validation of these two models against laboratory tests for Toyoura sand under monotonic and cyclic loading. Then, the performance of the two approaches is compared for the case of a seismic wave loading passing through a saturated soil column with different relative densities, revealing several differences between the results of the two models.