A theoretical model is established to study the direct transmission of sound through a finite cylindrical double shell. Shells comply with DONNELLS's equations and the theory include constantly spaced stiffeners in axial and circumferential directions. However this is limited in the case of large number of stiffeners. The acoustical excitation is a plane wave located in an infinite medium outside the shell. The two internal media are homogeneous. Absorption is taken into consideration by a complex wave number. The fluid structure coupling is exactly modelised and mechanical links between shells are constant distributed stiffness along circumferential lines. The solution of the equations is obtained by a modal method. Numerical results show the comparison between structural linkage and air gap effects on the transmission of sound inside the inner cavity.