Geology

Yucca Mountain is composed of mostly a substance called Welded Tuff (shown below).  This material is a volcanic rock that has been compressed for thousands of years and is very solid.  Nuclear waste would be put into canisters and then into holes dug into this stuff.

Although there doesn't seem to have been any movement in the area for the last 10000 years, that doesn't mean that there will be in the next 10000 years.  Earthquakes and such are never predictable and the only way to be safe seismically is to analyse the area around it and see how frequent they do come.