AbstractThis study deals with boundary‐layer flow on continuous solid surfaces. Flow of this type represents a new class of boundary‐layer problems, with solutions substantially different from those for boundary‐layer flow on surfaces of finite length. In this paper the boundary‐layer behavior on continuous surfaces is examined, and the basic differential and integral momentum equations of boundary‐layer theory are derived for such surfaces. In subsequent papers these equations will be solved for the boundary layer on a moving continuous flat surface and a moving continuous cylindrical surface, for both laminar and turbulent flow in the bound