The problem of transmission of acoustic waves through submerged orthotropic spherical shells was considered. The sound radiation in an infinite acoustic fluid is induced by a rigid spherical transducer, concentric within an orthotropic spherical shell having an axisymmetric surface‐velocity distribution. The space between the spherical transducer and the orthotropic spherical shell is full of the same acoustic fluid as that outside of the shell. The equations of motion for orthotropic shells, as well as for the fluid inside and outside, were derived. These equations are then solved by satisfying the continuity conditions on all solid‐fluid interfaces. Four representative transducer surface‐velocity distributions were considered. The solution for the farfield acoustic pressure was obtained for an orthotropic and for an isotropic shell.