AbstractAn oncoming two‐dimensional laminar boundary layer that develops an unstable inflection point and becomes three‐dimensional is described by the Hall‐Smith (1991) vortex/wave interaction equations. These equations are now examined in the neighbourhood of the position where the critical surface starts to form. A consistent structure is established in which an inviscid core flow is matched to a viscous buffer‐layer solution where the appropriate jump condition on the transverse shear stress is satisfied. The final result is a bifurcation equation for the (constant) amplitude of the wave pressure. A representative classical velocity profile is considered to illustrate solutions of this equation for a range of values of the wave‐numbers.