Experimental and numerical quasi-static and high strain rate tests, including compression, indentation and direct impact, were performed on a cellular concrete in order to investigate the effect of strain rate on the compressive strength. The results of compression tests indicated three distinct regions of the compressive strength dependence on strain rate. A relatively lower strain rate dependent compressive stress was found in the quasi-static strain rate-regime, 2x10-3-2x10-1 s-1, a relatively high strain rate dependent compressive stress in the dynamic strain rate-regime, 180-103 s-1 and a cut-off strength above 103 s-1. The dynamic increase factor (DIF=dynamic/static fracture strength) varied between 1 and 2.5 from quasi-static to dynamic strain rate-regime with a sharp increase after about 100 s-1. The indentation tests using 25 and 30 mm-diameter indenters in the quasi-static strain rate-regime (uniaxial state of strain) and resulted in moderate DIF values (1-1.13), very similar with those of the quasi-static compression tests (1-1.15). In the indentation tests, the DIF values significantly and also confirmed the numerically determined DIF values of concrete at 1000 s-1 (~1.30) without radial and axial inertia. The compression and direct impact tests in the Split Hopkinson Bar (SHPB) set-up were implemented numerically in LS-DYNA using an anisotropic strain rate insensitive material model, MAT_096 (MAT BRITTLE DAMAGE). The stress readings were performed at the specimen different locations of the SHPB and indicated that radial and axial inertia were dominant between 1 and 30 m s-1 (30-1000 s-1).