Gas sorption and its induced volumetric strain can significantly influence gas flow in coal by controlling the change in the conductivity of coal cleats. A significant number of studies have been conducted to date to describe the coal swelling stress with sorbing gases and several theoretical models have been proposed to estimate swelling stresses. Despite these efforts, the accurate prediction of coal swelling stress remains a challenge hence a comprehensive theoretical and experimental investigation of swelling stress is required. This is particularly important when swelling stress of fractured coals develops under external loading. We, therefore, perform two sets of time-dependent diffusion and volumetric strain experiments under various stress conditions and gas pressures on coal specimens (a highly cleated and a dense sample) exposed to helium and carbon dioxide. These experiments are conducted to investigate i) the performance of commonly used theoretical models for swelling stress estimation, ii) the validity of thermodynamics swelling coupling coefficient defining the swelling stress and iii) the effect of external stress on coal volumetric strain response (hydromechanical versus swelling/shrinkage). Our analysis shows that the developed models based on non-equilibrium thermodynamics can predict both the evolution and the final swelling stress closely. We further show that the new definition of swelling coupling coefficient leads to greater performance of non-equilibrium thermodynamics-based models and further suggest a new experimental technique for characterizing this coupling coefficient. Finally, the results reveal that the effect of external stress on the hydromechanical volumetric strain of coal (during gas adsorption by unloading and desorption by loading) has a considerable hysteresis, especially at high pore pressures.