We have developed a simple method of measuring the thrust of a jet by projecting it downwards into a liquid in a weighed vessel. The validity of this instrument has been confirmed using water. The thrusts for polymer solutions were measured to obtain the first normal stress differences, and it was concluded that the normal stress difference of dilute polymer solutions is correlated with the shear rate at low shear rates, but is a function of the mean velocity at high shear rates. Both the jet thrust and the friction factor of tube flow for very dilute polymer solutions were measured in laminar and turbulent flow regimes, and it was found that the estimated normal stress was rather small in comparison with the drag reduction effect. We discussed the correlation between the first normal stress difference and the velocity, assuming that a balance is attained among the elastic forces produced by each elastic stress at the entrance region, the fully developed flow region and the exit region of the tube flow, and obtained the result that the first normal stress difference is a function of velocity. This was confirmed with the experimental result of a surfactant solution.