  We study the propagation of bubbles of new vacuum in a radially inhomogeneous
Lemaitre-Tolman-Bondi background that includes a cosmological constant. This
exemplifies the classical evolution of a tunneling bubble through a metastable
state with curvature inhomogeneities, and will be relevant in the context of
the Landscape. We demand that the matter profile in the LTB background satisfy
the weak energy condition. For sample profiles that satisfy this restriction,
we find that the evolution of the bubble (in terms of the physically relevant
coordinates intrinsic to the shell) is largely unaffected by the prsence of
local inhomogeneities. Our setup should also be a useful toy model for
capturing the effects of ambient inhomogeneities on an inflating region.
