Bistable　composite　cylindrical　structures　have　been　developed　over　the　last　four　decades,　and　show　great　potential　for　shape　morphing　applications,　especially　in　aerospace.　Their　bistabilities　are　known　to　be　induced　by　unsymmetric　composite　layups,　while　the　governing　factors　on　shape　geometries　and　viscoelastic　mechanics　remain　an　enigma.　Here,　we　investigated　the　intricate　relationship　between　structural　geometry　and　stable　mechanics　of　a　bistable　unsymmetric　composite　cylindrical　structure.　A　polylactic　acid　(PLA)-based　carbon　composite　laminate　was　prepared　through　3D　printing,　which　released　design　freedom　on　structural　fiber　volume　fraction　that　could　be　controlled　by　modulating　hatch　spacing　between　the　composite　yarns.　This　strategic　adjustment　allowed　the　regulation　of　grid　density,　hence　the　in-plane　stress　level,　which　dominates　the　bistable　geometries.　The　cylindrical　composite　samples　were　produced　with　hatch　spacing　changed　from　1.25　to　5　mm,　corresponding　to　a　fiber　volume　fraction　ranged　from　24.2%　to　6.6%,　where　the　structural　curvature　was　also　changed　by　up　to　50%　difference　and　gradually　became　viscoelastic　dependent.　It　is　found　that　the　internal　stress　difference　in　thickness　direction　dominates　the　structural　bistability,　and　there　is　a　threshold　value　on　the　stress　difference　magnitude　to　essentially　maintain　the　bistable　configurations.　These　findings　are　expected　to　facilitate　reversed　structural　design　and　manufacturing　of　the　bistable　cylindrical　shells　with　tailorable　stability,　and　promote　their　viscoelastic-based　large　shape　morphing　fatigue　life　predictions.Highlights　Bistable　composite　cylindrical　shells　were　produced　with　various　grid　density.　A　theoretical　model　was　established　to　predict　the　time-dependent　bistability.　Stress　difference　in　thickness　direction　dominates　the　structural　curvature.　Stress　contour　reveals　the　viscoelastic-dependent　bistable　mechanics.