A production method of a (meth)acrylic acid or an ester thereof, comprising a step of forming a distillation gas in a distillation column from a process liquid containing a (meth)acrylic acid or an ester thereof and allowing the distillation gas to turn into a condensate through a vertical multi-tube heat exchanger, wherein a vertical multi-tube heat exchanger is used which comprises: a tubular body, an upper tube plate and a lower tube plate arranged respectively on the upper end side and the lower end side of the tubular body, a plurality of heat transfer tubes erected between the upper tube plate and the lower tube plate, and lid sections arranged respectively on the upper side of the upper tube plate and on the lower side of the lower tube plate, and in which some of the plurality of heat transfer tubes have an upper end protruding above the upper tube plate, with the remaining being not protruding, and the number of non-protruding heat transfer tubes is 3 or more, the non-protruding heat transfer tubes are provided in a symmetric even arrangement on the upper tube plate surface and are provided in the central part on the upper tube plate and also in the outer circumferential part or near the outer circumferential part of the upper plate, and the distillation gas introduced into a receiving chamber formed by the upper tube plate and the lid section on the upper side of the upper tube plate is cooled in the course of passing through the heat transfer tube and turns into a condensate, a solution containing a polymerization inhibitor is introduced into the receiving chamber, and the solution containing the polymerization inhibitor coming into contact with the distillation gas in the receiving chamber flows down inside the non-protruding heat transfer tube from the upper tube plate after forming a liquid flow layer on the upper tube plate. a tubular body, an upper tube plate and a lower tube plate arranged respectively on the upper end side and the lower end side of the tubular body, a plurality of heat transfer tubes erected between the upper tube plate and the lower tube plate, and lid sections arranged respectively on the upper side of the upper tube plate and on the lower side of the lower tube plate, and in which some of the plurality of heat transfer tubes have an upper end protruding above the upper tube plate, with the remaining being not protruding, and the number of non-protruding heat transfer tubes is 3 or more, the non-protruding heat transfer tubes are provided in a symmetric even arrangement on the upper tube plate surface and are provided in the central part on the upper tube plate and also in the outer circumferential part or near the outer circumferential part of the upper plate, and the distillation gas introduced into a receiving chamber formed by the upper tube plate and the lid section on the upper side of the upper tube plate is cooled in the course of passing through the heat transfer tube and turns into a condensate, a solution containing a polymerization inhibitor is introduced into the receiving chamber, and the solution containing the polymerization inhibitor coming into contact with the distillation gas in the receiving chamber flows down inside the non-protruding heat transfer tube from the upper tube plate after forming a liquid flow layer on the upper tube plate.