This report is described mainly about the measuring methods developed and results obtained by the author on the elasticity in water flow and dilute polymeric liquid flow at high strain rates: Jet thrust/reaction was measured for the flow through capillaries or orifices of small size and the elastic stress was calculated and the thrust/reaction was found to decrease significantly both for polymeric liquid flow accompanied with vortices upstream of the orifice and for water flow through micro-orifices. Elongational stress estimated using the measured thrust/reaction was revealed to be correlated with the flow velocity through orifices. This suggests that these fluids posses a property of elastic solid, not of viscoelastic liquid, under the present experimental condition. It was also shown that the pressure drop of the water flow through micro-orifices is much reduced and this was again explained by the elasticity. The model of elastic fluid possessing only elastic property without viscosity was proposed, Bernoulli's theorem was extended to the one including the elastic property, and several experimental phenomena characteristic of viscoelastic fluids were explained by this extended theorem. Additionally, the property of vortices for polymeric liquids was discussed.