The problem of the scattering of a steady plane acoustic wave by a spherical elastic shell is considered. A procedure is proposed for constructing an approximate solution, based on matching the expansions for different asymptotic models of the interaction of the shell with the acoustic medium. In the neighbourhood of zero frequency and thickness-resonance frequencies, long-wave low-frequency approximations of the equations of the theory of elasticity (the Kirchhoff-Love theory of shells or its refinement) and long-wave high-frequency approximations respectively are employed. Outside these neighbourhoods a flat-layer model is used. A comparison with the exact solution confirms that the proposed approached enables one to describe, with a uniform small error, the scattered pressure and the resonance components of the partial modes over a fairly wide frequency band.