  In this paper, the solutions of the pure geometric thick $f(R)$ brane are
investigated. The formulation of $f(R)$ is chosen as
$f(R)=\sum_{i=1}^{n}a_{i}R^{i}+\Lambda$. For the certain value of $n$, the
brane solution can be calculated, and when $n=3$, $n=4$, and $n=10$, the thick
brane solutions are presented. The solutions is stable under linear tensor
fluctuation. The zero mode of gravity and scalar field can be localized on
thick $f(R)$ branes naturally. The zero mode of vector field and left-chiral
fermion can be localized on thick $f(R)$ branes by introducing the coupling
with scalar curvature $R$ of spacetime, and the massive resonant modes can be
quasilocalized on the brane with the large coupling coefficients.
