Gradual simplifications of the mathematical model of a fixed-bed single reactor pass are presented. The purpose of the step-by-step model reduction was to answer the question to what extent it is necessary and/or possible to simplify the model to obtain the results which would be reliable and practically applicable for the purpose of modelling the complete industrial SO2 oxidation plants. The plant contains a multi-pass fixed-bed reactor. At present such a reactor can have four to five passes (beds). Each bed is 0.5 to 1 m high, of diameter from 5 to about 12 m. Such beds have dominant dynamics for the plant as a whole. It should be remembered, however, that there are some other elements of significant dynamics (i.e., heat exchangers) and that they also should be included in the simulation model of the complete plant. Thus, the reactor model should be as simple as possible to reduce the computing time. A heterogeneous, spatially two-dimensional model, including diffusion and reaction occurring inside the catalyst particles, was taken as a first approximation (Model 0). Additionally, the idea of how to incorporate heat accumulation in the reactor body into this model was presented. As the first step of the reduction of the model radial mass and heat transport as well as the internal diffusion inside the catalyst particle were neglected. The catalyst pore diffusion model was replaced by an experimental formula describing the effective rate of reaction (Model I). The lack of any concentration differences between the bulk gas and the surface of the catalyst particle, together with the lack of the axial dispersion term in the mass balance were assumed to be the next step of the model reduction. Thus such a model was pseudo-homogeneous with respect to the mass and heterogeneous with respect to the heat balance (Model II). The lack of temperature differences between the gas and solid was considered to be the last step of the model simplification (Model III). Subsequent steps of the model reduction were supplemented with appropriate comments, based on the author＇s own experience and some results of computer simulations published elsewhere [1-3]. There was presented the discussion of the influence of some phenomena occurring in unsteady state at the catalyst surface, which can have a significant effect on the amount of heat accumulated in the catalyst bed. Analysis of our own thermogravimetric results as well as those published by Brotz et al. [24, 25] support the view that these phenomena can significantly enhance (even by several times) the heat accumulated in the bed in the unsteady state. On the other hand, this can strongly influence the model-time scale. Referring to the model reduction the review of the models selected from the literature was presented. It was shown that except for the initial form of the model (Model 0), which is too complicated to be used in practical applications, basically every other form of the simplified model can be found in the literature. It was concluded that for practical applications of the simulation of the unsteady states in stationary fixed-bed reactors or nonstationary reverse flow reactors, the simplification to the form of the Model II seems to be quite admissible. On the other hand, the form of a fully homogeneous model (Model III) is too simplified and can give incorrect numerical results.