The non-linear quasi-static and dynamic elastic behaviour of Berea sandstone has been experimentally analysed showing hysteresis and a strong influence of moisture especially in the lower saturation range. It is shown that non-linear hysteretic response originates within the "bond system" of the material, that includes microcracks, intergrain contacts, asperities, dislocations, ... Hysteresis or non-classical non-linear behaviour is explained by the fact that the defects do not open and close at the same pressure. In dynamic loading a small number of these defects are activated explaining the higher stiffness compared to quasi-static loading, where a lot of defects are closed or opened. These effects can be adequately described in the framework of the so-called P-M (Preisach-Mayergoyz) space model. In the framework of poromechanics we show that the moisture influence on the non-linear elastic behaviour cannot be described by the effective stress concept. Two coupling coefficients (a classical and non-classical) are introduced to describe the fluid-solid coupling. These coupling coefficients are found not to be uniquely proportional to the degree of saturation (or volumetric water filling of the pore structure). The analysis of the experimental data show that, in the fine pore range situated in the bond system (clay, silica glue) where high fluid-solid interaction forces take place, the coupling coefficient increases proportional with fluid saturation. However, in an intermediate pore range the coupling coefficients decrease indicating less solid-fluid interaction in the coarse pore structure.