Fetal head moulding is a phenomenon which may contribute to satisfactory progress during delivery as it allows the fetal head to accommodate to the geometry of the passage. In contrast, excessive head moulding may result in cranial birth injuries and thus affect the infant shortly or even long after birth. One group of researchers in the past investigated the biomechanics of fetal head moulding from an engineering point of view and limited themselves to a static, linear model of the parietal bones. In this paper, we present a non-linear model of the deformation of a complete fetal skull, when subjected to pressures exerted by the cervix, during the first stage of labour. The design of the model involves four main steps: shape recovery of the fetal skull, the generation of a valid and compatible mesh for finite element analysis (FEA), the specification of a physical model and the analysis of deformation. Results of the analysis show good agreement with those obtained from clinical experiments on the quantitative assessment of fetal head moulding. The model also displays shapes after moulding which have been reported in previous studies and which are generally known in the obstetric and paediatric communities.