We have measured the reaction SO3+H2O+M-->H2SO4+M in a flow tube reactor in the pressure range between 31 and 260 mbar of synthetic air carrier gas. SO3 has been produced in the flow tube using a radical source for production of OH, which was converted to SO3 by reaction with SO2. The concentration of SO3 as well as the concentration of the reaction product has been measured by chemical ionization mass spectrometry (CIMS). Evidence has been found for the product being H2SO4. With increasing H2O-concentration in the flow reactor, an exponential decrease of the concentration of SO3 accompanied by a corresponding rise of the H2SO4-concentration has been observed. A detailed flow analysis has been carried out and the rate constants have been corrected for diffusive effects. The effect of heterogeneous reactions on the flow reactor walls has been investigated and could partially be quantified. From the experiment, values for the reaction rate constant in the range between 0.72 and 1.39 X 10(-15) cm(3) s(-1) have been inferred. These values are thought to be due to gas phase reactions only. Within the experimental accuracy the reaction rate constant did not undergo a significant pressure variation. The mean rate constant averaged over the total pressure range is (1.2 +/- 0.2) x 10(-15) cm(3) s(-1).