Functional magnetic resonance imaging (fMRI)is a principal method for mapping the human brain. fMRI data consist of a sequence of MR scans of the brain acquired during stimulation of specific cortical areas, and the purpose of analysing the data is to detect activated areas, i.e. areas where the intensity changes according to the stimulation paradigm. A common analysis procedure is to estimate the activity pattern non-parametricly by smoothing the data spatially. The focus is then on assessing significance of peaks or clusters in the smoothed activation surface by means of multiple hypothesis testing, rather than assessing the uncertainty of the estimated pattern itself. In this paper we formulate a more structured model for the spatial activation pattern. We achieve this by considering a stochastic geometry model where the activation surface is given by a sum of Gaussian functions, which to some extent can be thought of as individual centres of activation in the brain. The model is formulated in a Bayesian framework, where the prior distribution of the centres is given by a marked point process density. An advantage of this approach is that inference can be carried out by simulation techniques, and hence it is easy, though time consuming, to evaluate the uncertainty of the estimate or to test hypotheses of interest regarding the activation. Furthermore in this framework, we are able to model the temporal pattern of the activation with fewer assumptions than usually imposed. This reveals significant non-stationarities in the analysed data, which violate the common assumption of stationarity of the haemodynamic response.