Evaluation of the dynamic properties of quasi-brittle materials is of the utmost importance for assessing the vulnerability of structural components under dynamic loadings such as collision or explosion. To investigate the dynamic strength of (quasi)-brittle material, three-point bending tests are performed on a modified Split Hopkinson Pressure Bar. Such an apparatus is often used with pre-cracked specimen to determine the dynamic stress intensity factor of metallic materials. With quasi-brittle materials special care has to be paid to the processing of the test since fracture can occur at very low strains. The specimen remains in an out-of equilibrium state and fracture occurs before the support reactions appear as if it was a support-free impact test. A special non-equilibrium analytical approach has been developed to process the tests. Finite-element simulations are used to assess relevance of the proposed analysis for normalized short beams. Experimental results on brick and concrete samples showing a significant dynamic strength increase are presented.