Comprehensive understanding of the dynamics of the processes taking place in the testing specimen is available only by solving partial differential equations by finite element or finite differences method. However, even for small practical problems they appear to be of little effectiveness because of great computer resource (time and memory) usage. The situation can be improved by developing efficient algorithms of numerical modelling, based on a deeper analysis of the wave propagation phenomenon. As a result of the analysis, the finite element procedure in regular and free triangular finite element meshes was developed and adopted for the short wave propagation modelling during the ultrasonic measurement processes.