A production method of a (meth)acrylic acid or an ester thereof, comprising a step of, under a reduced pressure created by a pressure reducing device, forming a distillation gas 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 the vertical multi-tube heat exchanger comprises a tubular body, an upper tube plate and a lower tube plate arranged respectively on an upper end side and a lower end side of the tubular body, a plurality of heat transfer tubes erected between the upper tube plate and the lower tube plate, an upper lid section provided on an upper side of the upper tube plate, a lower lid section provided on a lower side of the lower tube plate, a receiving chamber surrounded by the upper tube plate and the upper lid section, an extraction chamber surrounded by the lower tube plate and the lower lid section, a junction port provided in the lower lid section, to which a suction pipe connecting the vertical multi-tube heat exchanger and the pressure reducing device is joined, and a baffle plate (27, 27', 27") provided in the extraction chamber and having a vertical plate section facing the junction port, and the distillation gas and a liquid containing a polymerization inhibitor are introduced into the receiving chamber, the distillation gas is cooled in the course of flowing inside the heat transfer tube to produce a condensate, and the condensate and uncondensed distillation gas flow into the extraction chamber, an area of the vertical plate section of the baffle plate (27, 27', 27") is larger than an opening area of the junction port, a top plate section is provided to connect the upper edge of the vertical plate section and an inner wall of the lower lid section, the uncondensed distillation gas within the extraction chamber flows into a relay space surrounded by the baffle plate (27, 27', 27") and the inner wall of the lower lid section and flows out to the suction pipe from the relay space via the junction port, the liquid containing a polymerization inhibitor is sprayed as drops from an atomizing nozzle into the receiving chamber, an atomizing nozzle where when water is sprayed from the atomizing nozzle under the same conditions as in the case of spraying the liquid containing a polymerization inhibitor from the atomizing nozzle into the receiving chamber, the Sauter mean diameter of water drops sprayed becomes from 570 to 1,500 μm is used as the atomizing nozzle, and an average gas flow velocity of the uncondensed distillation gas flowing into the relay space from the extraction chamber is 15.0 m/s or less. the vertical multi-tube heat exchanger comprises a tubular body, an upper tube plate and a lower tube plate arranged respectively on an upper end side and a lower end side of the tubular body, a plurality of heat transfer tubes erected between the upper tube plate and the lower tube plate, an upper lid section provided on an upper side of the upper tube plate, a lower lid section provided on a lower side of the lower tube plate, a receiving chamber surrounded by the upper tube plate and the upper lid section, an extraction chamber surrounded by the lower tube plate and the lower lid section, a junction port provided in the lower lid section, to which a suction pipe connecting the vertical multi-tube heat exchanger and the pressure reducing device is joined, and a baffle plate (27, 27', 27") provided in the extraction chamber and having a vertical plate section facing the junction port, and the distillation gas and a liquid containing a polymerization inhibitor are introduced into the receiving chamber, the distillation gas is cooled in the course of flowing inside the heat transfer tube to produce a condensate, and the condensate and uncondensed distillation gas flow into the extraction chamber, an area of the vertical plate section of the baffle plate (27, 27', 27") is larger than an opening area of the junction port, a top plate section is provided to connect the upper edge of the vertical plate section and an inner wall of the lower lid section, the uncondensed distillation gas within the extraction chamber flows into a relay space surrounded by the baffle plate (27, 27', 27") and the inner wall of the lower lid section and flows out to the suction pipe from the relay space via the junction port, the liquid containing a polymerization inhibitor is sprayed as drops from an atomizing nozzle into the receiving chamber, an atomizing nozzle where when water is sprayed from the atomizing nozzle under the same conditions as in the case of spraying the liquid containing a polymerization inhibitor from the atomizing nozzle into the receiving chamber, the Sauter mean diameter of water drops sprayed becomes from 570 to 1,500 μm is used as the atomizing nozzle, and an average gas flow velocity of the uncondensed distillation gas flowing into the relay space from the extraction chamber is 15.0 m/s or less.