A number of studies show that adsorption of small amount of water causes significant reduction of elastic moduli and increase of elastic wave attenuation in sandstones. This effect is of practical importance for near‐surface seismic studies and for applications of conventional rock physics theories, which require measurements of elastic properties of dry rock. Additionally, adsorption of water causes deformation of porous materials and rocks, which can be explained by the concept of varying surface stress, or change in the pressure of fluid adsorbed in pores. In this work we suggest that the adsorption‐induced elastic weakening of sandstones is caused by changing fluid pressure in compliant pores on grain contacts. In order to validate this concept, we conduct simultaneous measurements of the elastic moduli and deformation of the Bentheim sandstone with adsorption and desorption of water and observe ~20% change in the bulk and shear moduli accompanied with the strain of the order of 10−4. Then, we estimate that the fluid pressure change should be of the order of several megapascals to cause such deformation. Comparison of the measured variations in the elastic moduli related to the estimated change in the fluid pressure with the stress dependency of the bulk and shear moduli in Bentheim sandstone shows a broad agreement of the two sets of measurements. A reasonable magnitude of the estimated fluid pressure change is consistent with the suggested hypothesis.