Rocks in the earth’s crust usually contain pores and cracks. We developed a cracked porous medium elastic wave theory by modifying Biot’s poroelastic wave theory to include the effects of cracks, adding the crack density and aspect ratio as two important parameters to the original theory. The new theory was applied to model multipole acoustic wave propagation along a borehole surrounded by a cracked porous formation. The modeling results showed that the multipole acoustic waveforms were significantly affected by the presence of cracks even when the formation had low permeability and porosity. Particularly, cracks can cause the monopole P- and Stoneley waves and the dipole flexural wave to have significant sensitivity to hydrocarbon saturation, suggesting use of the waveform characteristics for hydrocarbon detection in tight formations.