X-rayμCT imaging is a common technique that is used to gain access to the full-field characterization of materials. Nevertheless, the process can be expensive and time-consuming, thus limiting image availability. A number of existing generative models can assist in mitigating this limitation, but they often lack a sound physical basis. This work presents a physics-supervised generative adversarial networks (GANs) model and applies it to the generation of X-rayμCT images. FEM simulations provide physical information in the form of elastic coefficients. Negative X-rayμCT images of a Hostun sand were used as the target material. During training, image batches were evaluated with nonparametric statistics to provide posterior metrics. A variety of loss functions and FEM evaluation frequencies were tested in a parametric study. The results show, that in several test scenarios, FEM-GANs-generated images proved to be better than the reference images for most of the elasticity coefficients. Although the model failed at perfectly reproducing the three out-of-axis coefficients in most cases, the model showed a net improvement with respect to the GANs reference. The generated images can be used in data augmentation, the calibration of image analysis tools, filling incomplete X-rayμCT images, and generating microscale variability in multiscale applications.