  We study brane worlds in an anisotropic higher-dimensional spacetime within
the context of $f(R)$ gravity. Firstly, we demonstrate that this spacetime with
a concrete metric ansatz is stable against linear tensor perturbations under
certain conditions. Moreover, the Kaluza-Klein modes of the graviton are
analyzed. Secondly, we investigate thick brane solutions in six dimensions and
their properties. We further exhibit two sets of solutions for thick branes. At
last, the effective potential of the Kaluza-Klein modes of the graviton is
discussed for the two solved $f(R)$ models in higher dimensions.
