The effect of slight viscoelasticity on the hydrodynamic stability of a plane Poiseuille flow is investigated by the linearized method of small two‐dimensional disturbances. The resulting equation is that of Orr‐Sommerfeld, modified however by a non‐Newtonian term. The constitutive equation used to represent the response of the fluid is that of a second‐order fluid. The equations are solved numerically, and compared with the results of Thomas. The critical Reynolds number is found to be lowered as the magnitude of a non‐Newtonian parameter increased.