The effect of elasticity on the flow of Jeffrey fluid in a tube is investigated in the present paper. The problem is solved analytically for two different methods. In the first method, flux is calculated by taking the stress of the elastic tube into consideration and in the second method flux is obtained by considering the pressureradius relationship. The expression for flux is obtained as a function of inlet or outlet radius of the tube or pressure. Modified Poiseuille law for elasticity is derived. The famous Poiseuille law is recovered as a special case, by making (1/E) tends to zero. The effects of different parameters on the flux are discussed through graphs. The influence of Jeffrey parameter and Youngs modulus on flow quantities is significant. It is observed that inlet and outlet pressures have opposite behaviours on flux for a given radius of the elastic tube.