We present a description of a simulation program for the fluorescence detector (FD) of the Pierre Auger Observatory. The simulation chain covers in detail all the physical processes involved in the fluorescence technique, from the shower longitudinal profile in the atmosphere to ADC-traces in the data acquisition system of the telescopes. Steps in the simulation include the generation of fluorescence and Cherenkov light in the atmosphere, propagation of this light to the telescope aperture, ray-tracing of photons in the Schmidt optics of the telescopes, and finally, simulation of the response of the electronics and the multi-level trigger. As an example of the simulation's use we show the results of a calculation of the trigger efficiency of the FD as a function of cosmic ray energy. (c) 2005 Elsevier B.V. All rights reserved.5453632642