Solid stresses emerge as the expanding tumour displaces and deforms the surrounding normal tissue, and also as a result of intratumoural component interplay. Among other things, solid stresses are known to induce extensive extracellular matrix synthesis and reorganization. In the present study, we developed a mathematical model of tumour growth that distinguishes the contribution to stress generation by collagenous and non-collagenous tumour structural components, and also investigates collagen fibre remodelling exclusively due to solid stress. To this end, we initially conducted in vivo experiments using an orthotopic mouse model for breast cancer to monitor primary tumour growth and derive the mechanical properties of the tumour. Subsequently, we fitted the mathematical model to experimental data to determine values of the model parameters. According to the model, intratumoural solid stress is compressive, whereas extratumoural stress in the tumour vicinity is compressive in the radial direction and tensile in the periphery. Furthermore, collagen fibres engaged in stress generation only in the peritumoural region, and not in the interior where they were slackened due to the compressive stress state. Peritumoural fibres were driven away from the radial direction, tended to realign tangent to the tumour-host interface, and were also significantly stretched by tensile circumferential stresses. By means of this remodelling, the model predicts that the tumour is enveloped by a progressively thickening capsule of collagen fibres. This prediction is consistent with long-standing observations of tumour encapsulation and histologic sections that we performed, and it further corroborates the expansive growth hypothesis for the capsule formation.