The invention relates to a process and an apparatus for chemical smoothing of a plastic part (10) produced by selective layerwise consolidation of a construction material. The process comprises the steps of: temperature-controlling the plastic part to a first temperature; temperature-controlling solvent vapour (8) comprising a solvent to a second temperature; subjecting the plastic part (10) to the solvent vapour (8) temperature-controlled to the second temperature for a particular duration, wherein the subjecting of the plastic part (10) to the solvent vapour (8) has the result that an outer layer of the plastic part (10) is liquefied; and discharging at least a portion of the solvent vapour (8) after the particular duration, wherein the plastic part (10) is stationary from commencement of the temperature-controlling of the plastic part until termination of the discharging of the solvent vapour (8).