Near‐field ground motions from explosions are governed by hydrodynamics and nonlinear material response. However, the calculation of the response using hydrodynamic solvers to observational distances, where motions are elastic, is computationally challenging. In order to propagate explosion ground motions from the near‐source region to the far field, we developed a hybrid modeling approach with a hydrodynamic‐to‐elastic coupling in three dimensions. Near‐source motions are computed with a Eulerian hydrodynamics code with adaptive mesh refinement. Motions on a dense grid of points are saved, resampled, and then passed to an elastic finite‐difference code for seismic‐wave modeling. Our coupling strategy is based on the uniqueness theorem, where motions are introduced into the elastic code as time‐dependent boundary sources and propagate as elastic waves at much lower computational cost than with the hydrodynamics code. We developed and verified the methodology to compute the hydrodynamic responses in either 2D or 3D into the elastic region and pass these to the elastic solver as 3D boundary motions. The accuracy of the numerical calculations and the coupling strategy is demonstrated in cases with a purely elastic medium as well as a nonlinear medium. Importantly, we show that our hydrodynamics code can accurately model motions for shallow sources in an elastic medium including surface waves, which is essential to insure that near‐source motions are correct. An application of our hybrid modeling approach is shown for a problem with scattering by 3D heterogeneity. Our strategy is capable of incorporating complex nonlinear effects near the source as well as volumetric and topographic material heterogeneity along the propagation path to receiver, making it very powerful for modeling a wide variety of effects and providing new prospects for modeling and understanding explosion‐generated seismic waveforms.