New multiphysical computational models for simulation of regular open and closed-cell cellular structures behaviour under compressive impact loading are presented. The behaviour of cellular structures with fluid fillers under uniaxial impact loading and large deformations has been analyzed with the explicit nonlinear finite element code LS-DYNA. The behaviour of closed-cell cellular structure has been evaluated with the use of the representative volume element, where the influence of residual gas inside the closed pores has been studied. Open-cell cellular structure was modelled as a whole to properly account for considered fluid flow through the cells, which significantly influences macroscopic behaviour of cellular structure. The fluid has been modelled by applying a Smoothed Particle Hydrodynamics (SPH) method. Computational simulations showed that the base material has the highest influence on the behaviour of cellular structures under impact conditions. The increase of the relative density and strain rate results in increase of the cellular structure stiffness. Parametrical numerical simulations have also confirmed that filler influences the macroscopic behaviour of the cellular structures which depends on the loading type and the size of the cellular structure. In open-cell cellular structures with higher filler viscosity and higher relative density, increased impact energy absorption has been observed.