  In this paper, we construct round fold maps or stable fold maps with
concentric singular value sets introduced by the author on smooth bundles over
spheres or bundles over more general manifolds. The class of round fold maps
includes special generic maps on spheres and such maps have been constructed on
smooth bundles over standard spheres of dimensions larger than 1 and connected
sums of smooth bundles over standard spheres of dimensions larger than 1 whose
fibers are standard spheres, for example, in previous studies by the author. In
this paper, we obtain round fold maps and the diffeomorphism types of their
source manifolds which do not appear in these studies in new manners.
