Th　establishment　of　conventional　pressure　gradient　models　is　based　on　the　idea　that　the　cross　section　of　a　wellbore　is　round,however,　in　practical　situation,　the　cross　section　of　a　wellbore　is　elliptical　under　the　influence　of　non-uniform　in-situ　stresses.　The　flow　pattern　in　annular　space　of　an　elliptical　cross-section　wellbore　is　obviously　different　to　the　flow　pattern　in　annular　space　of　a　round　cross-section　wellbore.　Based　on　the　basic　equations　of　fluid　mechanics,　a　concept　of　“effective　hydraulic　diameter”　has　been　introduced　in　establishing　a　pressure　loss　model　of　annulus　flow　in　elliptical　wellbore.　Studies　showed　that　with　an　increase　in　the　ratio　of　long　radius　over　short　radius　of　an　elliptical　wellbore,　the　average　flowrate　in　the　annular　space　decreases,　and　the　annular　pressure　gradient　decreases　with　it.　The　greater　the　ratio　of　the　long　radius　over　the　short　radius　of　an　elliptical　wellbore,　the　more　obvious　the　grading　of　the　high　and　low　flowrate　areas　along　the　helix　direction　of　the　annular　space.　Furthermore,　compared　with　simulation　results　(using　the　CFD　software),　this　model　has　calculation　errors　that　are　in　a　range　of　less　than　±　10%.　Analyses　of　affecting　factors　indicated　that　when　other　conditions　remain　constant,　the　annular　pressure　gradient　of　a　elliptical　wellbore　increases　somewhat　linearly　with　increases　in　annular　flowrate　and　yield　point　and　consistency　index　of　the　fluid,　and　somewhat　exponentially　with　increases　in　flow　index.　The　model　established　based　on　the　studies　can　be　used　to　calculate　the　wellbore　pressure　of　an　elliptical　wellbore.　©　2018,　The　Editorial　Board　of　Drilling　Fluid　&　Completion　Fluid.　All　right　reserved.