Estimation of mechanical and physical rock properties is an essential issue in applications related to reservoir geomechanics. Carbonate rocks have complex depositional environments and digenetic processes which alter the rock mechanical properties to varying degrees even at a small distance. This study has been conducted on seventeen core plug samples that have been taken from different formations of carbonate reservoirs in the Fauqi oil field (Jeribe, Khasib, and Mishrif formations). While the rock mechanical and petrophysical properties have been measured in the laboratory including the unconfined compressive strength, Young's modulus, bulk density, porosity, compressional and shear -waves, well logs have been used to do a comparison between the lab results and well logs measurements. The results of this study revealed that petrophysical properties are consistent indexes to determine the rock mechanical properties with high performance capacity. Different empirical correlations have been developed in this study to determine the rock mechanical properties using the multiple regression analysis. These correlations are UCS-porosity, UCS-bulk density, UCS-Vs, UCs-Vp Es-Vs, Es-Vp, and Vs-Vp. (*). For example, the UCS-Vs correlation gives a good determination coefficient (R2= 0.77) for limestone and (R2=0.94) for dolomite. A comparison of the developed correlations with literature was also checked. This study presents a set of empirical correlations that can be used to determine and calibrate the rock mechanical properties when core samples are missing or incomplete.