Lagrangian analysis method is re-analyzed, in which by measuring the physical variables of each Lagrangian positions the other physical variables of these positions of the material is analyzed, and then the dynamic mechanical properties of materials can be determined. However, the existing Lagrangian analysis methods are still inadequate when the particle velocity is known. In this paper, a new Lagrangian analysis method, with only particle velocity known, is developed, which is called step by step method along the time. The method does not make any assumption, and it can solve the problem when only particle velocity wave profiles are measured. A set of experimental data of concrete under impact is processed with the method, and the corresponding strain wave, stress wave, and stress-strain relations of the whole process of loading and unloading are calculated. Thus the strain rate dependent elastic-elastic constitutive characteristics of the concrete are revealed.