An alignment system that employs jacking block assemblies and alignment posts around the periphery of the top plate of a nuclear reactor lower internals core shroud to align an upper core plate with the lower internals and the core shroud with the core barrel. The distal ends of the alignment posts are chamfered and are closely received within notches machined in the upper core plate at spaced locations around the outer circumference of the upper core plate. The jacking block assemblies are used to center the core shroud in the core barrel and the alignment posts assure the proper orientation of the upper core plate. The alignment posts may alternately be formed in the upper core plate and the notches may be formed in top plate.