Damage and failures in high-pressure equipment and in high-energy piping have increased significantly during the second part of the twentieth century, in spite of improved construction procedures and the high quality of materials used. The result has been a grave expansion in the number of fatal disasters and ecological catastrophes, and their harmful social and economic consequences. This trend is apparent from a brief analysis of extensively developing industrial activities in different countries of the world, such as chemical, refinery and gas-treatment enterprises, power and the nuclear power industry. The statistics of failures in these industries show that most of the damage was caused by systems of interacting flaws. To numerically tackle these problems a previously developed code by the authors, based on the Element Free Galerkin (EFG) solution of systems of strongly interacting static cracks, was modified and adapted for dynamic problems in fracture mechanics. Several numerical examples of single crack propagation under impulse loading are solved. Accuracy of the results is verified comparing several analytical and numerical methods. The developed method is then applied to the physical model of dynamic crack propagation in the field of interacting flaws.