The paper presents relatively simple formulations of the problem of acoustic scattering by elastic shells immersed in fluids, which can serve as a basis for efficient numerical models. The full rigorous formulation of the problem, which involves the Helmholtz equations for acoustic pressures in the fluids and the Navier equation for 3D displacements in the elastic material, is reduced to a boundary value problem only for the Helmholtz equations with effective boundary conditions relating the boundary pressures and normal displacements on both sides of the shell. To that end, the thin elastic shell is regarded as a neighborhood of its midsurface and the boundary values of the elastic quantities (displacements and stresses) are expressed via their values at the midsurface. The shell thickness is considered a small parameter. Special consideration is given to the cases of flooded and hollow shells. Under certain conditions, the problem is reduced to a system of hypersingular integral equations, appropriate for solving by the Boundary Element Method (BEM). The resulting numerical models are validated by the comparison with the exact solutions for the case of spherical elastic shells. In particular, the BEM numerical solutions reproduce the resonant peaks and dips of the exact solutions.
