TheR‐matrix formalism of nuclear reaction theory is applied to the classical problem of wave scattering by an obstacle, as exemplified by acoustic scattering from fluid spheres imbedded in another fluid. The modal mechanical impedance of the system is a meromorphic function of the WignerRtype, which may be represented by a Mittag–Leffler series exhibiting its poles. The scattering functionSn(a diagonalSmatrix) is represented in anexactfashion byR, and in the one‐level approximation it reduces to the analytic function we obtained in our previous studies, with resonance‐level shifts and widths introduced by theR‐matrix formalism. Absorption in the obstacle or in the medium causes further shifts and broadening of the widths. Graphs of theRfunction and of the modal resonances as found from various level approximations are displayed and discussed.