Linear and non-linear structural analyses can be solved using the finite element method (FEM) and other numerical techniques. A new applied element method (AEM) that can predict with a higher degree of accuracy the continuum and discrete behavior of structures has recently been developed. In AEM, elements sharing the same surface will have connectivity springs even if the shared surfaces are only a portion of the surface. The collapse phases of structures by using AEM can be tracked and monitored. In the current research, the application of AEM is demonstrated by a non-linear dynamic analysis for reinforced concrete (RC) columns and slabs subjected to blast loading. The available experimental works carried out by other researchers to study the impact of close-in blast loading on RC members are used for verification. A good correlation between the experimental and numerical results has been achieved.