A novel hybrid method is described for analyzing convex multilayered conformal array antennas. The hybrid method is based on the spectral domain approach in combination with the ray-based uniform theory of diffraction (UTD) method. The analysis is divided in two parts. First, the spectral domain approach is accelerated by using an asymptotic extraction technique where the extracted term of the Green's function is calculated using UTD. It is shown that this new approach results in significant acceleration of the existing spectral domain algorithm without losing accuracy. The modified spectral domain method is then used in the second part where generally shaped convex multilayered surfaces are analyzed by using sets of canonically shaped surfaces (spheres and/or circular cylinders). Their radii are obtained using the UTD formulation, which contains important information such as distance and curvature of the generally shaped surface along each geodesic. The results obtained using the new algorithm are compared to the available results (calculated and measured) for different conformal antennas, showing very good agreement.