This paper presents a method mathematical modelling of cocurrent multitubular fixed-bed reactors. The method is adapted to the most widespread type of industrial reactor design, i.e. the system fitted with disk-and-doughnut baffles. The proposed model makes it possible to estimate the influence of non-uniformity of the heat carrier flow on the reactor characteristics, taking into account the coolant streams by-passing via the tube-to-baffle clearances. Based on the model, the effect of the operating parameters as well as of some more important geometrical parameters of the reactor on an exemplary highly exothermic process of partial benzene oxidation to maleic anhydride is discussed.