From　biology　to　engineering,　while　numerous　applications　are　based　on　capillary　phenomena　in　tubes　having　roughened　surfaces,　such　as　blood　transport,　paper-based　rapid　diagnostics,　microfluidic　fuel　cells,　and　shale　gas　transport,　the　dynamics　of　such　capillary　flow　remains　poorly　understood.　We　present　a　theoretical　model　for　a　circular　undulated　tube　that　has　an　idealized　cosine-type　inner　wall　characterized　by　two　key　morphological　parameters:　undulation　amplitude　and　axial　wave　number.　With　the　tube　oriented　at　an　arbitrary　angle,　we　first　characterize　the　apparent　contact　angle　of　the　fluid　as　a　function　of　local　distortion　angle　and　then　establish　a　theoretical　model　involving　inertia,　viscosity,　and　gravity　to　describe　the　dynamics　of　capillary　flow.　A　dimensionless　number　combining　the　three　forces　is　introduced　to　quantify　their　influence.　The　model　predictions　reveal　that,　in　an　undulated　tube　with　large　wave　numbers,　the　capillary　height　in　equilibrium　state　is　generally　lower　than　that　in　a　smooth　tube　of　similar　dimensions,　whereas　the　reverse　holds　if　the　wave　number　becomes　relatively　small.　When　the　viscosity　of　fluid　is　sufficiently　small,　capillary　oscillation　in　an　undulated　tube　is　alleviated　relative　to　that　in　a　smooth　tube,　and　hence　stable　capillary　flow　forms　more　easily　in　the　former.　©　2021　Author(s).