The free transverse vibrations for the fundamental mode of a single-span tube containing a flowing fluid are investigated analytically and experimentally. An approximate solution of the differential equation of motion is made with an infinite power series. Care must be taken in evaluating the large-order determinant that appears so that erroneous results may be prevented. The solution indicates a slight decrease in frequency and no decaying vibration with an increase in flow rate that can be attributed to the flowing fluid for simply supported, fixed, and fixed-simple ends. For fixed-free ends a decaying vibration due to the flowing fluid is indicated and a slight frequency decrease. The experimental results agree reasonably well with these solutions, although the frequency decrease is within the experimental error. The theory neglects internal damping of the tube and “support” damping. The latter appears significant in magnitude and is evaluated for the constructions used. This paper shows the reason for the incorrect conclusions of previous paper and gives experimental results that tend to verify the analytical results presented here and those in another previous paper by a different procedure.