Considering the deficiency in the research on transient vibro-acoustic characteristics of cylindrical shell structures, a Jacobi-Ritz semi-analytic method for forced vibration sound radiation of cylindrical shells in time domain was proposed by combining Newmark-β integral method and Kirchhoff boundary element integral equation in time domain. Based on the theory of first-order shear deformation and the idea of element method, a calculation and analysis model of vibration acoustic radiation of cylindrical shell was established. Jacobi polynomial and Fourier series were used to represent the allowable functions of axial and circumferential displacement. The time domain response of forced vibration of cylindrical shell was calculated on the basis of the Rayleigh-Ritz method and Newmark-β integral method. Based on Kirchhoff integral equation, the time domain response of radiated noise was solved, and the acoustic radiation characteristics of forced vibration of cylindrical shell were analyzed. Compared with finite element method/boundary element method numerical results, the proposed method has the characteristics of good convergence and high precision. The peak value of acoustic response of cylindrical structures shifts to the left with the weakening of the boundary condition stiffness, and the vibration acoustic response decreases with the increase of the thickness. When the peak frequency of random load is close to the natural frequency of the structure, strong characteristic line spectrum appears in the acoustic response of the structure.