Under　creeping　flow　conditions,　the　steady　state　of　Newtonian　fluid　and　non-Newtonian　fluid　between　two　plates,　one　of　them　a　plane,　and　the　other　one　with　a　sinusoidal　profile　is　considered　in　the　paper.　The　streamlines　of　the　flow　are　obtained　from　an　exact　analytical　treatment　of　the　Stokes　equations　by　making　use　of　finite　element　methods　and　complex　function　theory.　Based　on　the　calculations,　the　formation　and　evolution　of　vortices　in　the　flow　are　visualized.　The　influence　of　the　plate　undulations,　Reynolds　number　and　shear-thinning　coefficient　on　the　film　flow　is　shown　by　parameter　studies.