To identify deterministic and random vibrations of a closed cylindrical shell with a regular orthogonal system of stiffeners (stringers and frames) the effective prediction method was worked out. This method is a generalization of the known method of space-harmonic expansion based on the theorem of Bloch-Floquet for a two-dimensional case. The method permits considering correctly the stiffener discreteness and their interaction with the shell through all the components of displacement. On the basis of the method worked out the task of determining the sound field inside the cylindrical volume bounded by the shell excited by the deterministic and random fields of external forces is solved. The high efficiency of the method permits making the prediction of the shell vibrations and of the sound pressure levels inside the volume with account for sound-insulating layers over a wide frequency range. Examples of predicting the strengthened shell vibrations at large aircraft fuselage parameters are given as well as the sound pressure levels inside it under the point force excitation and under excitation by the random field of wall pressure fluctuations of the turbulent boundary layer (within the limits of one of the representation of the space correlation spectrum).