The steady-state and transient vibration responses of a medium thick hemispherical shell are obtained based on semi-ana? lytical method. According to the first-order shear deformation theory， the energy expression of the spherical shell structure is de? duced. The Jacobi orthogonal polynomials and Fourier series are introduced to represent the axial and circumferential displacements of the hemispherical shell structure. The steady vibration response of the hemispherical shell is obtained by Ritz method. The re? sults are compared with the finite element method to verify the feasibility of the presented method in this paper. On this basis， the characteristics of steady and transient vibration of the hemispherical shell under different boundary conditions， truncated angle and shell thickness are summarized and analyzed.