Dynamic stress concentration and pore pressure concentration around an infinitely long cylindrical cavity of circular cross-section subjected to harmonic plane dilatational waves in fluid-saturated porous elastic half-space were obtained by a complex function method based on potential function and multi-polar coordinate. The steady state Biot’s dynamic field equations of porous elastic solid with a viscous liquid were uncoupled into Helmholtz equations via given potential functions. A circular cavity with large radius is used to replace the straight boundary of the saturated porous elastic half-space. The stresses and pore pressures were obtained by using complex functions in multi-polar coordinates with certain boundary conditions of the solid matrix and the fluid matrix. The approximate solutions were compared to existing numerical solutions. Then the variations of the coefficients of dynamic stress concentration and the pore pressures concentration on boundaries of the cavity were discussed with different parameter conditions. The results of the given numerical example indicate that the method used is useful and efficient to the scattering and dynamic stress concentration of plane dilatational waves in saturated porous elastic half-space.