MIRI, the Mid-InfraRed Instrument, is one of four instruments being built for the James Webb Space Telescope, and is developed jointly between an European Consortium and the US. In this paper we present a software data simulator for one of MIRI's four instruments: the Integral Field Unit (IFU) Medium Resolution Spectrometer (MIRI-MRS), the first mid-infrared IFU spectrograph, and one of the first IFUs to be used in a space mission. To give the MIRI community a preview of the properties of the MIRI-MRS data products before the telescope is operational, the Specsim tool has been developed to model, in software, the operation of the spectrometer. Specsim generates synthetic data frames approximating those which will be taken by the instrument in orbit. The program models astronomical sources and generates detector frames using the predicted and measured optical properties of the telescope and MIRI. These frames can then be used to illustrate and inform a range of operational activities, including data calibration strategies and the development and testing of the data reduction software for the MIRI-MRS. Specsim will serve as a means of communication between the many consortium members by providing a way to easily illustrate the performance of the spectrometer under different circumstances, tolerances of components and design scenarios.