The acoustic P-waves velocity VP is measured in a water saturated fine-grained granite as a function of pore pressure for a series of confining pressures ranging from 10 to 75 MPa. Prior to VP measurements, different crack contents were generated in the granite specimens by means of controlled thermal pre-treatments at 450, 510, and 555 ¿C. VP variations are interpreted as resulting from crack behavior evolution in response to imposed pressures. An effective pressure law with an effective pressure coefficient close to 0.9 is derived for VP from a delimited pressure domain. This behavior is interpreted in terms of crack deformation under pressure. ¿ 2000 American Geophysical Union