A 3D semiconductor memory device including a plurality of memory cell strings, includes a substrate and a channel that extends from the substrate. Memory cells may be disposed in layers in which the diameter of the channel varies. A programming verification operation may be carried out in a sequence whereby memory cells more likely to fail in programming are verified before attempting to verify memory cells that are less likely to fail programming. In an exemplary embodiment, the verification operation is performed on a memory cell disposed in a layer associated with a larger-diameter channel before performing the verification on a memory cell disposed in a layer associated with a smaller-diameter channel. In an exemplary embodiment, if a verification process detects a programming failure, the verification of subsequent memory cells is cancelled.