Deformations of drops and bubbles opposed by surface tension and driven by radiation stresses at the interface are calculated using spherical harmonic expansions for the radial and tangential stresses. Superposed acoustic waves produce stresses which oscillate at the difference frequency ω of the waves in addition to static stresses. When the effects of viscosity on the acoustic waves are omitted. the tangential radiation stress vanishes; a procedure is proposed for calculating the radial stresses from the theory for “Acoustic Radiation Pressure on a Compressible Sphere” [K. Yosioka and Y. Kawasima, Acustica5, 167–173 (1955)]. The calculation of the response assumes incompressible second‐order flow and omits the body forces which are normally associated with acoustic streaming. Resonance phase shifts and enhancements of the response should occur when ω is close to the natural oscillation frequency of a mode. Quadrupole resonance phase shifts and enhancements have been observed [P. L. Marston and R. E. Apfel, J. Acoust. Soc. Am.63, S41(A) (1978): J. Colloid Interface Sci.68, 280–286 (1979)]. [Work performed at Yale University and supported by ONR.]