One of the complexities of geomechanical study is in the classification of rock’s properties and overpressured intervals—a knowledge which is not only essential for well safety and cost-effective drilling, but crucial in evaluating exploration risk factors and ensuring a successful hydraulic fracturing program. In this study, a more robust prediction of reservoir pressure regime is presented, where the geomechanical distributions of the rock give a distinct correlation. Three wells from the Niger Delta Basin were studied using empirical equations to estimate the elastic properties, wave velocities and the rock physics parameters for each well. From the results obtained, the velocities of compressional wave (Vp) and shear wave (Vs) decrease as porosity increases. Also, a linear correlation exists between Poisson’s ratio and Vp/Vs, where both variables showed distinct behavior and similar trend serving as useful tools for lithology identification. Another significant observation is the acoustic impedance of the materials which decreases with increasing porosity. Meanwhile, the depth plot of the impedance showed divergence and scattering away from the supposed linear trend. While inhomogeneity of the rock materials and disequilibrium compaction of sediments may account for this scattering, the variation of geomechanical distributions in this study revealed that pore pressure has a first order effect on the elastic strength of formations, also, under normal pore pressure conditions, acoustic impedance increases linearly with depth.