As PARTof an investigation (1) into the nature of a boundary layer existing at free edges of greatly deformed elastic plates, an approximate solution is obtained for a flat plate deformed into a conical frustrum. If the deformed plate is accurately conical, applied bending and normal shearing stress resultants are required at the edges, together with either an applied membrane stress resultant there, or an applied non-uniform pressure on the surface of the cone. In the absence of these applied loads deviations from the true conical shape occur. It is found that, if the plate is sufficiently thin, these deviations are confined to a boundary layer at each free edge, similar to that discussed by Fung and Wittrick (5). It is thus shown that such a boundary layer can apply to the interior of the plate, not only an edge bending stress resultant, as in (5) but also normal shearing and membrane stress resultants. In an appendix is given the inextensional solution for conical deformations of plates.