This work presents results of an experimental and theoretical study on dynamic and quasi-static failure of rocks and concrete. The results of dynamic compression and splitting of rocks (gabbro, granite, marble), as well as dry, water-saturated and frozen limestone and concrete are discussed. The tests were conducted using the Split-Hopkinson pressure bar with the diameter of 20 mm. It is shown that one material (or its condition) can have a lower dynamic strength for a higher static strength compared to the other material (or its condition). Also, it is shown a dependence of the threshold limit stress on the stress pulse duration. An unified interpretation of the experimental results, based on the structural-temporal approach is presented.