In this study, we investigate the ability of variational physics-informed neural networks (VPINNs) to learn complex fracture processes in anisotropic media. VPINNs have recently been explored in the context of crack propagation in isotropic brittle solids, demonstrating key fracture mechanisms such as crack nucleation, propagation, kinking, branching, and coalescence through phase-field damage modelling, which represents the current state of the art [1]. However, their extension to crack propagation in anisotropic materials remains an open research challenge, which this work seeks to address. Unlike the second-order approximations used for isotropic cases, modelling anisotropic crack propagation in the phase-field framework requires fourth-order approximations of fracture energy [2]. This is accomplished by using quadratic mesh elements to compute higher-order gradients. A neural network is then trained to minimise the system’s variational energy computed via finite element (FE) calculations. The proposed methodology is applied to several benchmark problems, such as a 2D square plate under pure tension and 2D L-shaped section with the right side forced upward. The results are shown to be in both qualitative and quantitative agreement with FE solutions, demonstrating the effectiveness of the approach.