A framework for modeling the transient response of percussive drilling systems is presented. The proposed approach is based on the distributed transfer function method (DTFM), which is a semi-analytical modeling technique. Experimental results obtained from a percussion testbed for the Regolith and ice drill for the exploration of new terrains (TRIDENT) were incorporated into this modeling technique. DTFM is shown to be a convenient, modular modeling approach, capable of handling complex boundary conditions and drill rod geometries. Moreover, this technique is computationally simple and allows for straightforward incorporation of experimentally measured boundary forcing via numerical convolution, as well as control of the frequency content in the transient response. An experimental study is used to demonstrate the ability of the proposed approach to characterize unknown boundary conditions.