In recent years, a kind of novel cellular concrete, fabricated by spherical saturated superabsorbent polymers, was developed. Its compressive behavior under high strain rate loadings has been studied by split Hopkinson pressure bar equipment in previous research, which revealed an obvious strain rate effect. It has been found by many researchers that the dynamic increase factor (DIF) of compressive strength for concrete-like materials measured by SHPB includes considerable structural effects, which cannot be considered as a genuine strain rate effect. Based on the extended Drucker-Prager model in Abaqus, this paper uses numerical SHPB tests to investigate structural effects in dynamic compression for this novel cellular concrete. It is found that the increment in compressive strength caused by lateral inertia confinement decreases from 5.9 MPa for a specimen with a porosity of 10% to 2 MPa for a specimen with a porosity of 40% at a strain rate level of 70/s, while the same decreasing trend was found at other strain rate levels of 100/s and 140/s. The lateral inertia confinement effect inside the cellular concrete specimen can be divided into the elastic development stage and plastic development stage, bounded by the moment dynamic stress equilibrium is achieved. The results obtained in this research can help to obtain a better understanding of the enhancement mechanism of the compressive strength of cellular concrete.