This invention relates to a polymerization reaction apparatus which is composed of a vertical cylindrical vessel, a rotating shaft inside the vessel, a plurality of agitating blades attached to the shaft, and a large number of plate-like heat transfer elements attached to the inner wall of the vessel, disposed radially between the agitating blades, and internally equipped with a passage for a heat transfer fluid, and in which apparatus a polymerizing mass passes through a gap between the rotating shaft, the agitating blades, and a large number of the plate-like heat transfer elements and exchanges heat with a heat transfer fluid circulating inside the plate-like heat transfer elements, effecting uniform removal of the reaction heat or uniform heating of the polymerizing mass and preventing vertical mixing.