A　new　reliability-based　topology　optimization　method　for　compliant　mechanisms　with　geometrical　nonlinearity　is　presented.　The　aim　of　this　paper　is　to　integrate　reliability　and　geometrical　nonlinear　analysis　into　the　topology　optimization　problems.　Firstly,　geometrical　nonlinear　response　analysis　method　of　the　compliant　mechanisms　is　developed　based　on　the　Total-Lagrange　finite　element　formulation,　the　incremental　scheme　and　the　Newton-Raphson　iteration　method.　Secondly,　a　multi-objective　topology　optimal　model　of　compliant　mechanisms　considering　the　uncertainties　of　the　applied　loads　and　the　geometry　descriptions　is　established.　The　objective　function　is　defined　by　minimum　the　compliance　and　maximum　the　geometric　advantage　to　meet　both　the　stiffness　and　the　flexibility　requirements,　and　the　reliabilities　of　the　compliant　mechanisms　are　evaluated　by　using　the　first　order　reliability　method.　Thirdly,　the　computation　of　the　sensitivities　is　developed　with　the　adjoint　method　and　the　optimization　problem　is　solved　by　using　the　Method　of　Moving　Asymptotes.　Finally,　through　numerical　calculations,　reliability-based　topology　designs　with　geometric　nonlinearity　of　a　typical　compliant　micro-gripper　and　a　multi-input　and　multi-output　compliant　sage　are　obtained.　The　importance　of　considering　uncertainties　and　geometric　nonlinearity　is　then　demonstrated　by　comparing　the　results　obtained　by　the　proposed　method　with　deterministic　optimal　designs,　which　shows　that　the　reliability-based　topology　optimization　yields　mechanisms　that　are　more　reliable　than　those　produced　by　deterministic　topology　optimization.　©　(2014)　Trans　Tech　Publications,　Switzerland.