Accumulative flow of gas into a vacuum tube has been studied. An analytical model, based on Fick's second law and assuming a constant diffusion coefficient, has been developed to describe the pressure response as a function of time and tube axial position for a constant gas flow rate into a closed vacuum tube. The predicted non-linear pressure response was verified by conducting short-term experiments involving a constant gas flow into an instrumented vacuum tube. Initially, the error in flow rate determined using the pressure rise technique was as much as +/- 100%. At longer time intervals, the constant diffusion coefficient assumption is invalid and the empirical model of Knudsen is used to describe the dependence of the diffusion coefficient on pressure. The governing partial differential equation was solved numerically. The numerical solution accurately predicts the pressure response at any time interval.