Nematic　liquid　crystal　elastomers　(LCEs)　contract　in　the　director　direction　but　expand　in　other　directions,　perpendicular　to　the　director,　when　heated.　If　the　expansion　of　an　LCE　is　constrained,　compressive　stress　builds　up　in　the　LCE,　and　it　wrinkles　or　buckles　to　release　the　stored　elastic　energy.　Although　the　instability　of　soft　materials　is　ubiquitous,　the　mechanism　and　programmable　modulation　of　LCE　instability　has　not　yet　been　fully　explored.　We　describe　a　finite　element　method　(FEM)　scheme　to　model　the　inhomogeneous　deformation　and　instability　of　LCEs.　A　constrained　LCE　beam　working　as　a　valve　for　microfluidic　flow,　and　a　piece　of　LCE　laminated　with　a　nanoscale　poly(styrene)　(PS)　film　are　analyzed　in　detail.　The　former　uses　the　buckling　of　the　LCE　beam　to　occlude　the　microfluidic　channel,　while　the　latter　utilizes　wrinkling　or　buckling　to　measure　the　mechanical　properties　of　hard　film　or　to　realize　self-folding.　Through　rigorous　instability　analysis,　we　predict　the　critical　conditions　for　the　onset　of　instability,　the　wavelength　and　amplitude　evolution　of　instability,　and　the　instability　patterns.　The　FEM　results　are　found　to　correlate　well　with　analytical　results　and　reported　experiments.　These　efforts　shed　light　on　the　understanding　and　exploitation　of　the　instabilities　of　LCEs.