A method and an apparatus for continuously producing plastic board. To produce a board which is clear and smooth having excellent mechanical strength and heat resistance through simple operation, a polymerizable mixture is poured into a gap defined by two endless belts and gaskets that seal between both sides of the belts. The polymerizable mixture is passed through a plurality of vessels containing polymerization liquids that are maintained at ordinary temperature to 120 C and that are arranged juxtaposed to one another. The polymerizable mixture is pressed by hydraulic pressure. After the polymerization is finished, the polymer is cooled through a cooling vessel thereby to continuously produce a plastic board. The method and apparatus of the invention are suited for obtaining a plastic board by polymerizing a polymerizable mixture which consists of a polymerizable compound having high heat of polymerization, particularly a polymerizable compound having two or more alpha - beta unsaturated double bonds, an untraviolet ray absorbing agent such as benzophenone of an amount necessary to shield ultraviolet rays, and a radical polymerization initiator.