Alexandrov manifold means Alexandrov space which happens to be a manifold, i.e. the space of directions is homeomorphic to shpere. Sorry for introducing this new term.

For such a open manifold does the soul theorem holds? i.e. the manifold is homeomorphic to the disk bundle over it's soul?

There is an example of Alexandrov space which is homeomorphic to a mnfld, but it has points with space of directions NOT homeomorphic to a sphere...– Anton Petrunin Feb 17 '10 at 21:47