  We introduce two classes of spherically symmetric spacetimes having a thin
shell of matter, in non-quadratic F(R) theories of gravity with non-constant
scalar curvature R. In the first, the thin shell joins an inner region with an
outer one, while in the second it corresponds to the throat of a wormhole. In
both scenarios, we analyze the stability of the static configurations under
radial perturbations. As particular examples in spacetimes with a cosmological
constant, we present charged thin shells surrounding a non-charged black hole
and charged thin-shell wormholes. We show that in both cases stable solutions
are possible for suitable values of the parameters.
