Using a first principles total energy method, we have reproduced the o
bserved charge density wave (CDW) state of alpha-uranium (called alpha
(1)). This CDW is found to be a result of a Peierls-like transition, i
.e., by opening of partial gaps at the Fermi level. The part of the Fe
rmi surface affected by the distortion shows a strong nesting of fairl
y narrow f bands. In addition we suggest that the slightly modified al
pha(1) CDW state, which is called alpha(2) and is observed by cooling
the alpha(1) phase, is caused by a closely related mechanism, namely,
by a nesting of the Fermi surface in the b direction. This is consiste
nt with the observed CDW ordering.