The first structural model for saccular cerebral aneurysm growth is proposed. It is assumed that the development of the aneurysm is accompanied by a loss of the media, and that only collagen fibres provide load-bearing capacity to the aneurysm wall. The aneurysm is modelled as an axisymmetric multi-layered membrane, exposed to an inflation pressure. Each layer is characterized by an orientation angle, which changes between different layers. The collagen fibres and fibroblasts within a specific layer are perfectly aligned. The growth and the morphological changes of the aneurysm are accomplished by the turnover of collagen. Fibroblasts are responsible for collagen production, and the related deformations are assumed to govern the collagen production rate. There are four key parameters in the model: a normalized pressure, the number of layers in the wall, an exponent in the collagen mass production rate law, and the pre-stretch under which the collagen is deposited. The influence of the model parameters on the aneurysmal response is investigated, and a stability analysis is performed. The model is able to predict clinical observations and mechanical test results, for example, in terms of predicted aneurysm size, shape, wall stress and wall thickness.