This paper models a railway carbody as a non-circular cylindrical shell with simply-supported ends, where the shell does not have end plates or other equipment attached. Transfer matrix method (TMM) was applied to the analysis of three-dimensional elastic vibration problems on this carbody. A 1/12 size carbody model was made for experimental studies to verify the validity of the numerical simulation. This model has end plates and was placed on soft sponge at both ends to simulate the freely-supported condition. Modal analysis was applied to the experimental model, and natural frequencies and mode shapes of vibration were measured. Comparing the results by TMM and experiments, the natural frequencies and mode shapes of vibration for lower modes show good agreement in spite of the differences in boundary conditions. The effect of stiffening members installed on the experimental model was also investigated.