SuperNEMO is an upcoming double-beta decay experiment designed to search for the hypothetical process of neutrinoless double-beta decay. It is composed of a double-beta emitting isotope surrounded by a tracking volume. This tracking volume is in turn composed of an array of drift tubes operating in the Geiger mode. To provide an accurate simulation of the experiment, it is important to understand the response of the drift tubes. In this study, the response of both the anode and cathode are considered. Two simulation models, called the timemap model and the two-dimensional fit model, have been developed to simulate the anode response. The timemap model is shown to be in good agreement with simulations made using the drift tube simulation software Garfield. The simulation models have been implemented as C++ packages that can be used as part of the SuperNEMO simulation. Both the models have been compared to data taken using a prototype module with 18 drift tubes.