Rocks in the earth’s crust usually contain pores and cracks. Typical examples include tight sandstone and shale rocks that have low porosity but contain abundant microcracks. By extending the classic Biot’s poroelastic wave theory to include the effects of cracks, we obtain an elastic wave theory for porous rocks containing cracks, adding crack density and aspect ratio as two important parameters to the original theory. Because the flat- or narrow-shaped cracks can easily deform under acoustic wave excitation, the acoustic property of a cracked porous rock is quite different for different saturation conditions. The predicted fluid sensitivity is used to interpret acoustic velocity log data from tight sand and shale gas formations. In both scenarios, the new theory correctly predicts the trend of velocity variation with gas saturation. The results confirm that the presence of cracks in tight rocks can give rise to significant hydrocarbon signature in the acoustic measurement data, allowing for identifying hydrocarbons from the data.