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