Process and apparatus for the (co) polymerization of styrene. The process is carried out by employing a liquid polymerization reaction mixture that includes styrene, in a mechanically stirred reactor in the form of a vessel comprising a side wall having the shape of a cylinder of revolution with a vertical axis (A), a bottom head and a top head that are joined to the side wall. The vessel is provided with a mechanical stirring device comprising (i) a central shaft of vertical axis coincident with the axis (A), connected to a drive system comprising a motor for rotating the central shaft, (ii) at least one baffle attached to the vessel. The baffle is away from the side wall of the vessel and takes the form of a cylinder of vertical axis and of rhomboidal cross section.