A clamping apparatus includes a frame adapted for mounting on a forklift so as to be raised and lowered along a mast of the forklift, a carriage supported by the frame for movement with respect to the frame in the widthwise direction of the forklift, two lifting arms supported by the carriage and extending in the widthwise direction of the frame, and a drive mechanism operatively connected to one of the lifting arms for producing relative movement of the lifting arms in the fore-and-aft direction of the frame to enable the lifting arms to grasp and release a load. The clamping apparatus can lift a portion of the objects in a closely-spaced layer and remove them from the layer without disturbing other objects in the layer. The clamping apparatus is particularly suitable for handling buckets.