Deciphering　the　mechanisms　underlying　the　high　sensitivity　of　cells　to　mechanical　microenvironments　is　crucial　for　understanding　many　physiological　and　pathological　processes,　e.g.　stem　cell　differentiation　and　cancer　cell　metastasis.　Here,　a　cytoskeletal　tensegrity　model　is　proposed　to　study　the　reorientation　of　polarized　cells　on　a　substrate　under　biaxial　cyclic　deformation.　The　model　consists　of　four　bars,　representing　the　longitudinal　stress　fibers　and　lateral　actin　network,　and　eight　strings,　denoting　the　microfilaments.　It　is　found　that　the　lateral　bars　in　the　tensegrity,　which　have　been　neglected　in　most　of　the　existing　models,　can　play　a　vital　role　in　regulating　the　cellular　orientation.　The　steady　orientation　of　cells　can　be　quantitatively　determined　by　the　geometric　dimensions　and　elastic　properties　of　the　tensegrity　elements,　as　well　as　the　frequency　and　biaxial　ratio　of　the　cyclic　stretches.　It　is　shown　that　this　tensegrity　model　can　reproduce　all　available　experimental　observations.　For　example,　the　dynamics　of　cell　reorientation　is　captured　by　an　exponential　scaling　law　with　a　characteristic　time　that　is　independent　of　the　loading　frequency　at　high　frequencies　and　scales　inversely　with　the　square　of　the　strain　amplitude.　This　study　suggests　that　tensegrity　type　models　may　be　further　developed　to　understand　cellular　responses　to　mechanical　microenvironments　and　provide　guidance　for　engineering　delicate　cellular　mechanosensing　systems.　©　2017　International　Committee　on　Composite　Materials.　All　rights　reserved.