In this paper, we are interested in a mathematical analysis of a simplified 1D mechanical model for the interaction between a mallet and an elastic membrane. First, using elementary mathematical techniques, we study quite precisely the case where the mallet is in interaction with a rigid body. This analysis allows us to understand the influence of physical parameters on the mallet behavior. Then, we show how the results of this study can be extended to the case where the mallet is in interaction with a membrane.