Compressional and shear slowness, which are derived from dipole sonic logs, are two important parameters that can be used for determining physical rock properties, such as Young's modulus and Possion's ratio. Since the dipole sonic logs are not common in oil fields and may be ran just in a few oil wells of a field, modeling the compressional and shear slowness indirectly seems to be a key approach in obtaining the required data for calculating mechanical properties. An integrated approach used in this study is an error minimization-based technique that consists of basic petrophysical relationships accompanied by a neuro fuzzy inference system, each of which being assigned a weighting factor. To verify the performance quality of the method, it is applied to an Iranian heterogeneous carbonate reservoir and then is compared by the measured compressional and shear slowness. Achieved results showed that the integrated model provides more accurate results in comparison with other modeling techniques. Results obtained by an integrated approach can be used to determine Young's modulus and Possion's ratio, which are two critical parameters for geomechanical applications.