This study established an energy radiation transfer model for constant curvature shell structures to predict the energy response of structures under high-frequency radial point excitation. Based on Donnell-Mushtari thin shell theory, the vibration control equation of a constant curvature shell was derived and the wave propagation characteristic parameters were obtained. The directional function of the input power radiation intensity of bending waves was approximately obtained using the phase stationary method. The kernel functions of energy density and power flow intensity were obtained based on the energy density control equation. The energy at any point within the structure can be obtained by superposition the energy generated by the real source and the energy generated by the boundary virtual sources. The energy responses of three typical constant curvature shell structures were calculated, and the results were compared with the modal superposition method and vibrational conductivity approach to verify the accuracy of the proposed model. Finally, the influence of frequency, curvature radius, and damping on the energy response of constant curvature shell structures was discussed. Numerical results indicate that both curvature radius and excitation frequency can affect the wave propagation characteristics and energy distribution of shell structures. The smaller the difference is in curvature radius in the   and   directions, the smaller the directionality of bending wave propagation; The smaller the curvature radius is, the higher the average energy density of the structure; The higher the frequency is, the less directional the propagation of bending waves, and the faster the decay rate of structural energy density.