It is well documented that disaccharides in general and trehalose (TRH) in particular strongly affect physical properties and functionality of lipid bilayers. We investigate interactions between lipid membranes formed by 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and TRH by means of molecular dynamics (MD) computer simulations. Ten different TRH concentrations were studied in the range wTRH = 0-0.20 (w/w). The potential of mean force (PMF) for DMPC bilayer-TRH interactions was determined using two different force fields, and was subsequently used in a simple analytical model for description of sugar binding at the membrane interface. The MD results were in good agreement with the predictions of the model. The net affinities of TRH for the DMPC bilayer derived from the model and MD simulations were compared with experimental results. The area per lipid increases and the membrane becomes thinner with increased TRH concentration, which is interpreted as an intercalation effect of the TRH molecules into the polar part of the lipids, resulting in conformational changes in the chains. These results are consistent with recent experimental observations. The compressibility modulus related to the fluctuations of the membrane increases dramatically with increased TRH concentration, which indicates higher order and rigidity of the bilayer. This is also reflected in a decrease (by a factor of 15) of the lateral diffusion of the lipids. We interpret these observations as a formation of a glassy state at the interface of the membrane, which has been suggested in the literature as a hypothesis for the membrane-sugar interactions.