Rock mechanical properties are critical parameters for many development techniques related to tight reservoirs, such as hydraulic fracturing design and detecting failure criteria in wellbore instability assessment. When direct measurements of mechanical properties are not available, it is helpful to find sufficient correlations to estimate these parameters. This study summarized experimentally derived correlations for estimating the shear velocity, Young's modulus, Poisson's ratio, and compressive strength. Also, a useful correlation is introduced to convert dynamic elastic properties from log data to static elastic properties. Most of the derived equations in this paper show good fitting to measured data, while some equations show scatters in correlating the data due to the presence of Calcite, Quartz, and clay in some core samples. Brittleness index (BRI) indicates ductile behavior of the core samples is also studied for the interested reservoir. The results of BRI show that the samplers range from moderate to high brittleness, and the difference in BRI comes from the presence of some minerals, as explained using the X-ray diffraction test (XRD). The proposed correlations are compared to other correlations from literature for validation, and the results of the comparison show good matching that explains the accuracy of the proposed equations.