Understanding the adsorption‐induced swelling in coal is critical for predictable and enhanced coal bed methane production. The coal matrix is a natural anisotropic disordered microporous solid. We develop an elastic transverse isotropic poromechanical model for microporous solids which couples adsorption and strain through adsorption stress functions and expresses the adsorption isotherm as a multivariate function depending on fluid pressure and solid strains. Experimental data from the literature help invert the anisotropic adsorptive‐mechanical properties of Brzeszcze coal samples exposed to CO2. The main findings include the following: (1) adsorption‐induced swelling can be modeled by including fluid‐specific and pressure‐dependent adsorption stress functions into equilibrium equations, (2) modeling results suggest that swelling anisotropy is mostly caused by anisotropy of the solid mechanical properties, and (3) the total amount of adsorbed gas measured by immersing coal in the adsorbate overestimates adsorption amount compared to in situ conditions up to ∼20%. The developed fully coupled model can be upscaled to determine the coal seam permeability through permeability‐stress relationships.