By　using　complex　function　theory　and　Finite　Element　Method,　creeping　drag　laminar　flows　of　Newtonian　and　Non-Newtonian　Fluids　between　plates　are　numerically　studied,　and　the　influence　from　Reynolds　Number,　shear-thinning　coefficient　and　blockage-passage　ratio　on　the　emergence　and　evolvement　of　vortex　is　analyzed.　Researches　indicate　that　with　some　qualifications,　the　increase　of　Reynolds　Number　also　would　bring　out　vortex　and　enlarge　the　areas　vortex　affects,　but　this　influence　is　limited.　The　reason　why　Reynolds　Number　is　not　the　key　factor　to　vortex　is　the　great　velocity　gradient　inside　the　flow.　With　different　profiles　of　substrate　plate,　the　influence　from　Reynolds　number　on　vortex　is　similar.　While　for　the　Non-Newtonian　Fluids,　shear-shinning　coefficient　puts　little　impact　on　the　flow　configuration,　but　its　augment　heightens　the　position　where　flow　separation　occurs　and　boost　up　the　range　and　intensity　of　vortex,　which　makes　the　flow　field　further　unsteady.　As　the　average　plate-distance　increases,　the　absolute　value　of　critical　waviness　also　enhances,　while　the　blockage-passage　is　on　the　contrary,　which　shows　that　critical　blockage-passage　trends　to　decrease　with　the　augment　of　waviness.