A　new　mathematical　model　was　developed　in　this　study　to　simulate　the　unsteady　flow　in　controlled　mud-cap　drilling　systems.　The　model　can　predict　the　time-dependent　flow　inside　the　drill　string　and　annulus　after　a　circulation　break.　This　model　consists　of　the　continuity　and　momentum　equations　solved　using　the　explicit　Euler　method.　The　model　considers　both　Newtonian　and　non-Newtonian　fluids　flowing　inside　the　drill　string　and　annular　space.　The　model　predicts　the　transient　flow　velocity　of　mud,　the　equilibrium　time,　and　the　change　in　the　bottom　hole　pressure　(BHP)　during　the　unsteady　flow.　The　model　was　verified　using　data　from　U-tube　flow　experiments　reported　in　the　literature.　The　result　shows　that　the　model　is　accurate,　with　a　maximum　average　error　of　3.56%　for　the　velocity　prediction.　Together　with　the　measured　data,　the　computed　transient　flow　behavior　can　be　used　to　better　detect　well　kick　and　a　loss　of　circulation　after　the　mud　pump　is　shut　down.　The　model　sensitivity　analysis　show　that　the　water　depth,　mud　density　and　drill　string　size　are　the　three　major　factors　affecting　the　fluctuation　of　the　BHP　after　a　circulation　break.　These　factors　should　be　carefully　examined　in　well　design　and　drilling　operations　to　minimize　BHP　fluctuation　and　well　kick.　This　study　provides　the　fundamentals　for　designing　a　safe　system　in　controlled　mud-cap　drilling　operatio.