The 34S34S and 13C13C isotopic fractionations in the OCS + OH reaction are investigated using RRKM-theory. The reaction proceeds via different channels, at low pressures a channel leading to CO + SOH dominates. While with increasing pressure an adduct forming channel becomes competitive. The resulting overall rate constant is not strongly dependent on pressure and agrees well with experiments. The competition between channels makes the fractionation constants highly pressure dependent, however the sulfur-34 fractionation constant varies only from about -5‰ to 0‰ in the troposphere and lower stratosphere. The carbon-13 isotopic fractionation is stronger; between -40‰ and -70‰ in the troposphere and lower stratosphere.