Catalyst deactivation is traditionally described with semi-empirical models involving separable kinetics and time-dependent activity factors, but the rational approach is to treat catalyst deactivation as a chemisorption process among other surface processes. The catalytic process A→R along with surface poisoning P+*→P* (* is an active site) was modelled for batch and continuous reactors. Simple semi-analytical mathematical solutions were obtained, which avoid the use of surface coverage in computations. Numerical simulations revealed the behaviour of the model in the parameter space. For batch reactors, the approach to a limit conversion as well as the increase of the apparent reaction order due to catalyst poisoning was illustrated. The model was applied to batchwise hydrogenation of sitosterol to sitostanol on a dispersed platinum catalyst and in the presence of a sulphurous poison. The behaviour of the system was successfully described with a simple, mechanistic model based on the adsorption-reaction-poisoning concept.