Accurately modelled computer-generated data can be used in place of real-world signals for the design, test and validation of signal processing techniques in situations where real data is difficult to obtain. Bio-signal processing researchers interested in working with fNIRS data are restricted due to the lack of freely available fNIRS data and by the prohibitively expensive cost of fNIRS systems. We present a simplified mathematical description and associated MATLAB implementation of model-based synthetic fNIRS data which could be used by researchers to develop fNIRS signal processing techniques. The software, which is freely available, allows users to generate fNIRS data with control over a wide range of parameters and allows for fine-tuning of the synthetic data. We demonstrate how the model can be used to generate raw fNIRS data similar to recorded fNIRS signals. Signal processing steps were then applied to both the real and synthetic data. Visual comparisons between the temporal and spectral properties of the real and synthetic data show similarity. This paper demonstrates that our model for generating synthetic fNIRS data can replicate real fNIRS recordings.