Abstract The mathematical modeling and computational simulation have been used as indispensable resource in the analysis of most processes, including catalytic reactors. Among the available tools for process representation. The fuzzy modeling has na increasing interest. The fuzzy logical is the logic that supports the reasoning manners that are approximate instead of exact. Fuzzy modeling of systems is a technique for the treatment of qualitative information in a rigorous way. Derived from the concept of fuzzy set, the fuzzy logical constitutes the base for the development of methods and modeling algorithms, allowing the reduction of the project complexity and implementation. The mathematical modeling of three-phase reactors is not still as developed as some other processes of the chemical industry. Therefore this work has as objective the development of a model mathematical of a three-phase system, using the foundations of group operations and fuzzy logical. The system in subject is a three-phase slurry catalytic reactor operating in steady-state regime, and with a tubular geometric configuration and refrigeration. The fuzzy model was able to represent very well.