This paper derives a wave function series expansion solution for the diffraction of incident-plane SV waves by an underground circular cavity in a saturated poroelastic half-space. The effects of the incident frequencies, incident angles, boundary drainage, porosity, and Poisson’s ratio on the diffraction of incident plane SV waves are discussed. It is shown that, depending upon the incident angles, the surface displacement amplitudes near the cavity in dry and saturated poroelastic half-spaces are very different, and large phase shifts can be observed. The Poisson’s ratio is also an important facto, and has a larger effect for the undrained saturated than for the drained saturated half-space. Large pore pressures are found near and around the cavity, and it depends strongly upon the incident angles. As the porosity increases, the pore pressure increases significantly, but its variations become smoother, and they become more complicated as the frequency increases. For large porosity, the effect of the drainage condition is significant, and for the same porosity the surface displacement amplitudes near the cavity in the undrained are larger than those in the drained saturated half-space.