Dynamical compressive testing of cement based materials' specimens were carried out on an experimental set-up realizing the traditional Kolsky technique, as well as, on a stand for testing standard cubic specimens under explosive loads. Determination of strengths of structural and sandy concretes and cement mortar in compression and development of stress-strain relationships, including post-failed parts, were the main aim of presented investigations. The experimental methods presented here enable conducting of strength testing of structural and sandy concrete, and cement mortar under dynamic loads at a predetermined velocity of load increase, during its increase up to the moment of specimen's fracture, as well as, to obtain post-failed stress-strain relationships.