Horiuti's generalized rate expression is derived by using a simple model of gas effusion and then developed for heterogeneous catalysis. Characteristics of his expression are pointed out. The expression is used for estimating a rate of hydrogen evolution theoretically by taking mutual repulsive interactions among reacting species into account statistical mechanically to overcome the difficulty Tafel faced with catalytic mechanism. Results calculated on Ni(1 1 1) plane satisfactorily reproduced the experimental data observed on Ni polycrystalline electrode. The last part reviews recent knowledge of the hydrogen evolution reaction at Pt low index planes from which we learn a new information entirely unexpected from a classical idea assuming a single kind of adsorbed hydrogen atom on the surface. (C) 2003 Elsevier Science B.V. All rights reserved.