The Leeb hardness test is a non-destructive and portable technique that can be used both in the laboratory and in-field applications. The main purpose of this study is to predict the dynamic elastic constants of the igneous and sedimentary rocks using Leeb dynamic hardness testing. For this purpose, three vital topics have been investigated and analyzed. First, the relationships between ultrasonic wave velocities and dynamic elastic constants with the Leeb hardness were investigated. Thereafter, by determining the rock quality index (IQ) using microscopic studies and by analyzing the quality index-porosity plot, the variation of the Leeb hardness values was studied. Eventually, the longitudinal waveform in rock samples with different quality indexes and Leeb hardness were analyzed. To achieve these outputs, 33 samples of igneous and sedimentary rocks with a wide range of physical, mechanical, and textural features were collected and tested. The results of the analyses show that in both igneous and sedimentary rocks, the dynamic modulus of elasticity (Ed) has a significant correlation with the Leeb hardness. Generally, based on the microscopic studies, it was observed that the existence of the porosity in sedimentary rocks and intracrystalline and intracrystalline fissures in igneous rocks sharply reduce the Leeb hardness and thus lead to changes in the form of the longitudinal waves.