An end of arm tool that is capable of handling fragile items such as eggs that are packaged in containers (e.g., egg cartons) that require special handling is provided. The end of arm tool comprises vacuum cup assemblies to grip the top surfaces of the packages, clamp fingers to clamp the edges of the packages, and optionally a pusher assembly to release the packages from the clamp fingers. In addition, a method of loading packages into cases using the end of arm tool apparatus of the present invention is provided. A gripper may be provided to place divider sheets between packages in the cases.