The interior boundary‐value scalar (acoustic) problem in the region between two spheres of radiiR1,R2and distancedbetween their centers is considered for both Dirichlet and Neumann boundary conditions. Surface singular integral equations are used to formulate the problem. Their solution is obtained in terms of spherical wave functions in combination with related addition theorems. It is then specialized to the case of small values forkd=2πd/λ to yield exact, closed‐form expressions for the coefficientsgnsin the resulting relations ωns(kd) =ωns(0) [1+gns(kd)2+⋅⋅⋅] for the resonant (natural) frequencies of the cavity. Numerical results, comparisons, and possible generalizations are also included.