The vapour expansion of extruded cereals is a versatile technique used in the food processing industry to produce a wide variety of light, crisp & crunchy products such as snacks, breakfast cereals and pet foods. The range of textures that can be produced depends on a complex interaction of a many parameters controlling the expansion phase making the development and optimisation of the process a difficult task involving many trials. This thesis is aimed at developing a numerical model of vapour expansion of extruded cereal to improve our understanding of the physical process and to help speed up the development of new products. Rather than try to model the growth of each bubble explicitly a more economical "micro-macro" approach was developed involving the coupling of a 1D model for single bubble growth with a CFD code for modeling the bulk fluid flow. Several bubble growth models have previously been developed and coupled with simplified models for the flow inside the die, but none of them have succeeded in predicting even the right trend in the observed dependence of the expansion with operating conditions. A microscopic model was first developed along similar lines to those described in the literature with some improvements and then coupled to different macroscopic flow models. Although the process requires at least a 2D coupling to properly capture the full behaviour of vapour expansion, considerable insight was gained by coupling with a 1D compressible macroscopic flow model assuming isotropic expansion in order to predict the evolution of the extrudate outside the die. In particular the 1D model predicted the growth and maximum extrudate diameter in qualitative agreement with experimental measurements and showed for the first time why the expansion is observed to be stronger with lower water content or lower temperature. It showed for example that increasing the water content influences the expansion more by changing the partition between lateral and longitudinal expansion than by changing the degree of volume expansion itself. In other words, the increased water content decreases the viscosity and increases the nucleation pressure so the expansion occurs sooner and more rapidly and hence spends more time expanding inside the die where it can only accelerate. There is thus less bubble growth remaining for lateral expansion by the time it reaches the die outlet. For very low moisture content the model predicts a weak reduction in lateral expansion due to the reduced availability of water for vaporization. The resulting peak was also observed experimentally. Two types of 2&3D coupling with the Fluent CFD code were developed and tested: 1) where the equations for the microscopic model are solved in Eulerian form as User Defined Scalar (UDS) equations and 2) where the microscopic model equations are solved in Lagrangian form along stream lines computed using the Discrete Phase Model (DPM). In both cases the free-surface expansion of the extrudate from the die is simulated with the Volume of Fluid (VOF) capability in Fluent. Unfortunately neither approach could be made to converge stably due to numerical problems that could not be rectified due to the closed source nature of Fluent. A similar problem with the 1D model was solved by deriving a more intimate coupling between the micro and macro equations to reduce their order.