We demonstrate the training of a generative adversarial network (GAN) for the prediction of optical property maps (scattering and absorption) using spatial frequency domain imaging (SFDI) image data sets that are generated synthetically with a free open-source 3D modelling and rendering software, Blender. The flexibility of Blender is exploited to simulate 5 models with real-life relevance to clinical SFDI of diseased tissue: flat samples containing a single material, flat samples containing 2 materials, flat samples containing 3 materials, flat samples with spheroidal tumours and cylindrical samples with spheroidal tumours. The last case is particularly relevant as it represents wide-field imaging inside a tubular organ e.g. the gastro-intestinal tract. In all 5 scenarios we show the GAN provides an accurate reconstruction of the optical properties from single SFDI images with a mean normalised error ranging from 1.0-1.2% for absorption and 1.1%-1.2% for scattering, resulting in visually improved contrast for tumour spheroid structures. This compares favourably with the ∼10% absorption error and ∼10% scattering error achieved using GANs on experimental SFDI data. Next, we perform a bi-directional cross-validation of our synthetically-trained GAN, retrained with 90% synthetic and 10% experimental data to encourage domain transfer, with a GAN trained fully on experimental data and observe visually accurate results with an error of 6.3%-10.3% for absorption and 6.6%-11.9% for scattering. Our synthetically trained GAN is therefore highly relevant to real experimental samples but provides the significant added benefits of large training datasets, perfect ground-truths and the ability to test realistic imaging geometries, e.g. inside cylinders, for which no conventional single-shot demodulation algorithms exist. In the future, we expect that the application of techniques such as domain adaptation or training on hybrid real-synthetic datasets will create a powerful tool for fast, accurate production of optical property maps for real clinical imaging systems.