It is *theoretically* possible for two siblings of the same sex to be identical, but not in a practical sense. For each of the 23 chromosomes you get from your mother, you get a random pick of the two homologs. So, for chromosome 1, there is a 50% chance you and your sibling get the same copy. read more
If those hyper-related siblings in turn mated with one another, after a few generations you’d have people giving birth to infants that were essentially genetic clones. However, such inbreeding appears to carry a number of potentially harmful consequences. read more