A semi-infinite periodic model of cylindrical shell of radial phononic crystals（ CS-RPCs） is constructed by alternate distribution of two homogeneous materials. A theoretical analysis of the propagation of radial waves from inside to outside is performed. The method of numerical analysis is used to discuss and analyze the appearance regularity of the surface localized modes with a finite period CS-RPCs. At the same time,the energy band structure is obtained by the eigenvalue method of the mechanical state vector total transfer matrix and then the numerical results are verified. Finally,the internal stress magnitude and distribution of the finite period CS-RPCs structure are analyzed in detail.The results show that the elastic band gap exists in the CS-RPCs,and the appearance of the surface localized modes is related to the wave velocity of the free surface. The stress concentration of radial phononic crystal structure is related to the wave velocity of loading surface.