As the interaction between tissue adaptation and the mechanical condition within tissues is complex, mathematical models are desired to study this interrelation. In this study, a mathematical model is presented to investigate the interplay between collagen architecture and mechanical loading conditions in the arterial wall. It is assumed that the collagen fibres align along preferred directions, situated in between the principal stretch directions. The predicted fibre directions represent symmetrically arranged helices and agree qualitatively with morphometric data from literature. At the luminal side of the arterial wall, the fibres are oriented more circumferentially than at the outer side. The discrete transition of the fibre orientation at the media-adventitia interface can be explained by accounting for the different reference configurations of both layers. The predicted pressure-radius relations resemble experimentally measured sigma-shaped curves. As there is a strong coupling between the collagen architecture and the mechanical loading condition within the tissue, we expect that the presented model for collagen remodelling is useful to gain further insight into the processes involved in vascular adaptation, such as growth and smooth muscle tone adaptation.