For the numerical simulation of the dynamic structural problems special attention is needed to be paid while choosing the time integration algorithm. The task becomes even more challenging if any non-linearity (especially the boundary non-linearities) is involved in the system. In the literature, a number of time integration algorithms are available. However, the choice of an appropriate time integration algorithm is an essential criterion to ensure the efficiency and the robustness of the numerical simulations. The difficulty in this choice resides in being able to combine the robustness, accuracy and the stability of the algorithm. Time integration algorithms are usually classified into two categories: (1) explicit and (2) implicit. For stability reasons, explicit algorithms use smaller time-step in comparison to implicit algorithms. Explicit algorithms are used for the multi-degree-of-freedom system having various non-linearities, e.g. geometrical, material and boundary, for which carrying out the iterations operation becomes prohibitively expensive, and convergence issues are frequent. In this contribution, the stability, robustness and the accuracy of popularly employed explicit time integration algorithms are investigated and compared through a number of single and multi-degree-of-freedom non-linear systems.