Mechanisms　of　adhesion,　rolling　and　detachment　of　cells　under　shear　flows　play　an　important　role　in　the　understanding　of　cell　adhesion　related　in　vivo　biological　processes　and　the　development　of　in　vitro　microfluidics.　Previous　researches　are　focused　on　cell　adhesion　under　uniform　flows,　though　accelerating　flows　are　common　in　microscale　flows　in　vivo　and　in　vitro.　Effects　of　flow　acceleration　on　cell　adhesion　and　detachment　remain　unknown.　As　such,　we　developed　a　mathematical　model　based　on　front　tracking　method　and　investigated　cell　adhesion　and　detachment　under　flow　acceleration.　The　main　findings　include:　1)　flow　acceleration　makes　it　more　difficult　for　cells　to　roll　and　detach,　2)　with　decreasing　flow　acceleration,　cell　deformation　and　the　critical　wall　shear　stress　for　cell　rolling　and　detachment　increases.