The snare drum is one of the more complex musical instruments from a modeling and synthesis perspective---it includes elements modeled as 0D (the drum stick), 1D (the snares), 2D (a pair of membranes) and 3D (the cavity and perhaps the surrounding space), as well as three specific forms of nonlinearity: that of the striking mechanism, the possibility of large amplitude vibration in the membranes themselves, as well as the distributed collision between the set of snares and the snare head. In this article, some preliminary modeling results will be presented, employing time-domain finite difference schemes for the membranes and snare set, and various different levels of modeling for the adjacent acoustic space, including a full 3D model involving absorbing boundary conditions, and simplified lumped representations of the interior derived from modal analysis. Simulation results and sound examples will be presented, and computational complexity wil be discussed.