An apparatus for transferring a pattern of minute surface structures, using a pair of press members which are located opposingly for movements toward and away from each other. One press member is adapted to support thereon a mold having on a transfer surface a master pattern of minute structures to be transferred, while the other press member is adapted to support thereon an annular substrate plate having a curable resin layer coated thereon and to press the resin layer against the transfer surface of the mold to transfer said minute structures to the resin layer. The mod is provided with a circular center hole defining at least three small-diameter segments and three large-diameter segments alternately and at uniform angular intervals along an inner periphery of the mold. The annular substrate plate has an inside diameter exactly matching with the small-diameter segments at the inner periphery of the mold. A chuck mechanism is provided inside of the lower press member, the chuck mechanism having at least three chuck pawls located in uniformly spaced positions along inner periphery of the substrate plate. The chuck pawls are radially displaceable to take either an operative position or a receded position, and are adapted to grip the inner periphery of the substrate together the small-diameter segments of the center hole of the mold at the time of setting the substrate plate in alignment with the mold, and to grip the inner periphery of said substrate plate alone, at spaced positions from the large-diameter segments of the center hole of the mold, at the time of separating the substrate plate from said mold.