The clinical management of aggressive brain tumours remains challenging, particularly due to their invasive nature and to the mechanical disruptions these lesions cause within the confined cranial space. The rapid expansion of these neoplasms can exert pressure on the adjacent tissue, displacing and deforming normal brain structures and potentially leading to severe neurological deficits. At the same time, the irregular growth patterns make full surgical removal difficult. Here, we present a mathematical and computational framework that predicts the progressive mechanical impact of expanding tumour masses on adjacent brain structures. Our formulation employs a sharp-interface approach to represent well-circumscribed, solid tumours whose expansion generates significant mechanical forces on the surrounding tissues. The biomechanical model, based on the theory of mixtures, allows us to describe both tissue elasticity and fluid stresses. Additionally, by integrating anisotropic growth distortions with imaging-derived white matter fibre orientations, our model accounts for preferential expansion patterns, which can lead to highly asymmetric tumour shapes. On the computational side, using Magnetic Resonance Imaging datasets, we generate three-dimensional reconstructions of cerebral architecture, including a representation of ventricular cavities, and use them for Finite Element simulations. This enables us to quantify how much an enlarging tumour compresses these structures and alters their morphology, possibly leading to clinical issues. Our framework is also capable of determining strain profiles throughout the affected tissues, identifying regions at risk for functional compromise. We also simulate different treatment regimes, combining radiotherapy and chemotherapy, to evaluate potential outcomes from various intervention strategies. Collectively, these capabilities may advance our understanding of tumour-tissue mechanics in the brain, emphasizing the importance of patient-specific anatomy and fibre-guided growth patterns in predicting deformations and stresses.