The stability of plane Poiseuille flow to finite disturbances was studied for the second order fluid using the cascade (Stuart‐Watson‐Reynolds‐Potter) method. The analysis was carried out for elasticity numbers up to10−4.In this range the Deborah number based upon disturbance propagation is small and the second order fluid is a consistent constitutive approximation. In contrast to linear theory in this region, elasticity has a stabilizing effect on finite disturbances relative to the Newtonian liquid and the difference between stability behavior of Newtonian and slightly elastic liquids tends to disappear.