This work concerns the prediction of potentially damaging thermoacoustic oscillations in gas turbine combustion systems by computational means. A framework is laid out to predict numerically the frequency and stability of thermoacoustic oscillations, with focus on the high frequency screech instability of afterburners. A hybrid numerical method is used that includes separate calculations of the mean flow and of the perturbed field due to the acoustic oscillations. This modularity supports the choice of models that are the most appropriate for combustion and for acoustic wave propagation, which are the processes that make up the feedback mechanism that can lead to the establishment of an instability. This gives flexibility, improved accuracy and more insight into the physics of the thermoacoustic system at a potentially reduced computational cost. The mechanism leading to screech involves the formation of vortices induced by acoustic transverse modes at the afterburner flameholder. These vortices trap fresh reactants that burn after a certain time delay, therefore feeding energy into the oscillation. Within a linear approximation, the effect of small amplitude acoustic fluctuations on the flame is studied by perturbing harmonically the transverse velocity at the flameholder lip over a range of frequencies using forced combustion CFD calculations. The response in heat release rate, which is a thermoacoustic source of sound, is represented by a flame transfer function (FTF). It is argued that for the investigation of screech oscillations, this FTF must be multidimensional because of the transverse nature of the acoustic oscillation. For fully premixed flames, the main contributor to heat release rate fluctuations is the variation in flame surface area. This information is used to develop a novel flame model that represents the multidimensional, frequency dependent response of the flame to velocity perturbations. Compared to FTFs, which require computationally expensive forced calculations, this model has the advantage of providing the frequency dependent flame response as part of the acoustic calculation. After verification and validation of each of the tools used for the acoustic and combustion simulations, this flame model is used in the analysis of a simplified afterburner, where a high frequency, radial and longitudinal resonant mode was computed. Convective modes, which are important in the prediction of the frequency of thermoacoustic oscillations are predicted as a result of the interaction between the acoustic wave and the flame.