  We consider a five dimensional warped spacetime where the bulk geometry is
governed by higher curvature $F(R)$ gravity. In this model, we determine the
modulus potential originating from the scalar degree of freedom of higher
curvature gravity. In the presence of this potential, we investigate the
possibility of modulus (radion) tunneling leading to an instability in the
brane configuration. Our results reveal that the parametric regions where the
tunneling probability is highly suppressed, corresponds to the parametric
values required to resolve the gauge hierarchy problem.
