A solution has been constructed for the transient motion of a viscoelastic cylindrical shell of the arbitrary cross section, surrounded by a fluid medium. The fluid region external to the shell is mapped into the interior of a rectangle. The transformed fluid equation together with the shell equations are expressed in finite-difference form and the time variable suppressed through the application of the Laplace transform. Shell displacements and acoustic pressures are found over the fluid field and at the fluid solid interface.

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