  In this paper, we consider viscoelastic flows in a rough domain (with typical
roughness patterns of size $\epsilon$ < 1). We present and rigorously justify
an asymptotic expansion with respect to $\epsilon$, at any order, based upon
the definition of elementary problems: Oldroyd-type problems at the global
scale defined on a smoothened domain and boundary-layer corrector problems. The
resulting analysis guarantees optimality with respect to the truncation error.
