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Mechanics of the bilayer membrane play an important role in many biological and bioengineering problems such as cell–substrate and cell–nanomaterial interactions. In this work, we study the effect of thermal fluctuation and the substrate elasticity on the cell membrane–substrate adhesion. We model the adhesion of a fluctuating membrane on an elastic substrate as a two-step reaction comprised of the out-of-plane membrane fluctuation and the receptor–ligand binding. The equilibrium closed bond ratio as a function of substrate rigidity was computed by developing a coupled Fourier space Brownian dynamics and Monte Carlo method. The simulation results show that there exists a crossover value of the substrate rigidity at which the closed bond ratio is maximal. [ABSTRACT FROM AUTHOR]