The asymptotical stability of wave patterns for viscous conservation laws is an interesting and important problem. Considerable progress on the stability of single shock wave, rarefaction wave in the whole space has been achieved in the past several decades. An interesting question is whether these wave patterns are still stable under periodic spatial perturbation. Compared with the stability problem in the whole space, the solution has no limit at the far fields. In this talk, I will present recent works on the stability of single shock wave and rarefaction wave for viscous conservation laws under periodic perturbations.