A carrier apparatus (6) simple and inexpensive in structure, and capable of assuring machining at high efficiency and high precision, in machining of a surface of a thin disk-shaped workpiece (W). In an apparatus for grinding the surface of a workpiece (W) while supporting and rotating a thin disk-shaped workpiece (W), the carrier apparatus (6) constitutes a workpiece rotation supporting device (5) for rotating and driving while positioning and supporting the circular outer circumference of the workpiece (W), and comprises an annular carrier main body (31) having a circular inner peripheral edge (31a) surrounding closely the whole circumference of the workpiece (W), and a notch trigger (32) having a pointed end engaging part (32b) to be engaged with a notch (Wn) in the workpiece (W), being formed as an integral piece, in which the notch trigger (32) is a separate part from the carrier main body (31), so as to be exchangeable and joined and fixed integrally, and the pointed end engaging part (32b) has a mounting structure of projecting inward in a radial direction from a part of the circular inner peripheral edge (31a) of the carrier main body (31).