The influence of combustor size and shape on material feasibility is explored using (structural and fuel) weight, as well as fuel economy as metrics. A materials selection methodology developed for actively cooled rectangular panels has been embellished to include cylindrical/annular configurations. The procedure incorporates an analytical model for temperature and stress distributions subject to thermomechanical loads representative of hypersonic flight conditions. The model has been numerically verified using finite element simulations. By combining the model with optimization routines, materials robustness maps have been produced, depicting the range of thermal loads and fuel flow rates that satisfy all design constraints. A wide selection of high-temperature materials has been investigated. Comparisons of cylindrical and rectangular combustors are made for the leading candidates. It is established that the cylindrical designs allow both lighter optimal structures as well as greater robustness and fuel economy.