Analytical expressions are derived for the acoustic resonance frequency shifts in a hard‐walled spherical cavity, caused by the introduction of an eccentric small inner sphere. A straight‐forward and simple approach is employed to obtain a first‐order perturbation of the cavity wave function and the corresponding resonant frequency shift. The results are useful in a variety of problems connected with acoustic levitation and with excitation or probing of resonant cavities. Graphical results for some of the lower‐order resonant frequencies are given for various values of the parameters.