We present and discuss the results of some numerical simulations dealing with wave motion in one-dimensional pantographic media, also known as pantographic beams. Specifically, the analysis is carried out in large displacements regime and pantographic beams are modeled by using a completely discrete approach. Nonlinear vibrations induced by a transversal impulse are studied. A simple yet efficient time-stepping scheme was used to reconstruct the motion and, consequently, to explore the propagation of strain waves in the pantographic medium. The numerical study concludes that the main features of the observed strain wave propagation are extremely useful toward the understanding of the dynamic behavior of the pantographic micro-structure and its continuum counterparts.