A local analysis has been made about a point at the free surface of an incompressible viscous fluid flow at steady state by means of series expansions of the Navier–Stokes equations. Dividing streamlines, curvature effects, and the role of vorticity have been studied. A single dividing streamline is always perpendicular to the free surface. This means, in particular, that all steady vortices with one end of their axes attached to a free surface are perpendicular to it. Double dividing streamlines of two‐dimensional viscous fluid flows at a free surface always have an angle of 90° between them, whereas double dividing streamlines of inviscid irrotational motion on a free or solid surface are separated by an angle of 60°. For an interface between two immiscible viscous fluids a novel ‘‘refraction law’’ for dividing streamlines has been derived.