A novel methodology for linear stability analysis of high-frequency thermoacoustic oscillations in gas turbine combustors is presented. The methodology is based on the linearized Euler equations (LEEs), which yield a high-fidelity description of acoustic wave propagation and damping in complex, nonuniform, reactive mean flow environments, such as encountered in gas turbine combustion chambers. Specifically, this work introduces three novelties to the community: (1) linear stability analysis on the basis of linearized Euler equations. (2) Explicit consideration of three-dimensional, acoustic oscillations at screech level frequencies, particularly the first-transversal mode. (3) Handling of noncompact flame coupling with LEE, that is, the spatially varying coupling dynamics between perturbation and unsteady flame response due to small acoustic wavelengths. Two different configurations of an experimental model combustor in terms of thermal power and mass flow rates are subject of the analysis. Linear flame driving is modeled by prescribing the unsteady heat release source term of the linearized Euler equations by local flame transfer functions, which are retrieved from first principles. The required steady-state flow field is numerically obtained via computational fluid dynamics (CFD), which is based on an extended flamelet-generated manifold (FGM) combustion model, taking into account heat transfer to the environment. The model is therefore highly suitable for such types of combustors. The configurations are simulated, and thermoacoustically characterized in terms of eigenfrequencies and growth rates associated with the first-transversal mode. The findings are validated against experimentally observed thermoacoustic stability characteristics. On the basis of the results, new insights into the acoustic field are discussed.