  The thick brane model is considered in $f(R)\sim R^n$ gravity. It is shown
that regular asymptotically anti-de Sitter solutions exist in some range of
values of the parameter $n$. A peculiar feature of this model is the existence
of a fixed point in the phase plane where all solutions start, and the brane
can be placed at this point. The presence of the fixed point allows to avoid
fine tuning of the model parameters to obtain thick brane solutions.
