Biot’s theory is employed to study the propagation of plane‐harmonic seismic waves in a transversely isotropic liquid‐saturated porous solid. Along withSHwave, the existence of three quasiwaves is discussed and analytical expressions for their velocities of propagation have been obtained. It has been observed that velocities of existing waves vary with the direction of propagation. Frequency equation for the propagation of Rayleigh‐type surface waves at the free surface of transversely isotropic liquid‐saturated porous solids has been obtained. Possibilities of existence of body waves and surface waves have been discussed numerically by assuming different sets of values of elastic constants. Dependence of the velocities of propagation on the direction of propagation has been exhibited.