In this paper, the Multi-Material ALE formulation is applied to simulate the propagation of an air blast through the atmosphere, and its reflection on an assumed rigid cylindrical obstacle. The mathematical and numerical implementations of this formulation are presented. In order to validate the formulation and prove its ability to capture the propagation and reflection of high pressure waves, comparisons of the simulations with the experimental blast pressure measured on an assumed rigid cylinder are performed. The simulation conducted via the presented models and methods gives good predictions for pressure time histories recorded on the rigid cylinder.