The Young’s modulus and Poisson’s ratio, parameters reflecting the elastic response of a rock to stress, are the key parameters used in many engineering activities, such as hard coal mining and natural gas extraction. The objective of this paper was to present the results of complex laboratory measurements of the static and dynamic Young’s modulus and Poisson’s ratio for Upper Carboniferous hard coals from the Upper Silesian Coal Basin. The coals differed in geologic age (Mudstone Series—younger coals; Upper Silesian Sandstone Series—older coals) and petrographic structure (vitrain, clarain, and durain lithotype). Elastic parameters of the coals were determined following compression tests under a complex state of stress, as well as using the ultrasonic method in reservoir conditions. On this basis, linear functional dependences between parameters such as UCS, differential stress, confining pressure, strain rate, P- and S-wave velocities, and the static and dynamic Young’s modulus and Poisson’s ratio were determined. These dependences turned out to be linear, with strong and very strong correlation, as indicated by the high coefficients of determination, R2. These new results significantly broaden the knowledge of elastic properties of Carboniferous hard coals, especially in the field of geoengineering, underground coal gasification, and reservoir stimulation for coal bed methane extraction.