The stability of the flow over a flat plate to finite amplitude disturbances is studied using a model by Milinazzo and Saffman [J. Fluid Mech.160, 281 (1985)]. The traveling wave solutions which bifurcate from the Orr–Sommerfeld neutral stability curve of the Blasius profile are calculated numerically. This curve is the intersection of the zero energy plane with a neutral stability surface in energy, Reynolds number, and wave‐number space. Although the bifurcation is supercritical at the ‘‘nose’’ of this curve, it is shown that it is subcritical elsewhere and that the minimum Reynolds number for the existence of traveling waves is less than the critical Reynolds number of the Orr–Sommerfeld neutral stability curve. This result suggests that finite amplitude disturbances can initiate transition.