The invention concerns a process and an apparatus for performing chemical reactions under pressure in the presence of a solid catalyst in a multi-stage reaction zone, after external intermediary thermal conditioning. This process may be used for the synthesis of ammonia or methanol or for gasoline reforming. It is characterized in that at least one reaction fluid is introduced into at least one compartment, a first reaction effluent is recovered, a heat exchange takes place, outside the reaction zone, between a first effluent and an external heat exchange medium, then said first effluent is introduced into at least one subsequent compartment and a second reaction effluent is recovered from said subsequent compartment. The reaction fluid or reaction effluent circulates cross-wise in the compartments substantially perpendicularly to the reaction zone, the compartments being tight and of elongate shape, each compartment being adjacent to one or two other compartments, each group of two adjacent compartments comprising a common partition, wall, either substantially parallel to said generatrix or substantially oblique with respect thereto.