The problem of the spherical acoustic resonator containing a slightly viscous medium is considered. Derivation of the equations of sound waves in a viscous medium is carried out, and it is shown that separation of the particle velocity into a divergenceless vector and a curl‐less vector gives rise to both a vector Helmholtz equation and a scalar Helmholtz equation. By using known solutions to these equations in spherical coordinates and imposing suitable boundary conditions, the frequencies of the free vibrations are calculated as well as the attenuation constants associated with each frequency. The effect of viscosity is, thus, seen to decrease slightly the natural frequencies and to cause a time rate of decay of the free vibrations. The attenuation constant for the purely radial modes of vibration is much smaller than that for modes having tangential velocity components.