The　purpose　of　the　present　work　is　to　study　the　buckling　problem　with　plate/shell　topology　optimization　of　orthotropic　material.　A　model　of　buckling　topology　optimization　is　established　based　on　the　independent,　continuous,　and　mapping　method,　which　considers　structural　mass　as　objective　and　buckling　critical　loads　as　constraints.　Firstly,　composite　exponential　function　(CEF)　and　power　function　(PF)　as　filter　functions　are　introduced　to　recognize　the　element　mass,　the　element　stiffness　matrix,　and　the　element　geometric　stiffness　matrix.　The　filter　functions　of　the　orthotropic　material　stiffness　are　deduced.　Then　these　filter　functions　are　put　into　buckling　topology　optimization　of　a　differential　equation　to　analyze　the　design　sensitivity.　Furthermore,　the　buckling　constraints　are　approximately　expressed　as　explicit　functions　with　respect　to　the　design　variables　based　on　the　first-order　Taylor　expansion.　The　objective　function　is　standardized　based　on　the　second-order　Taylor　expansion.　Therefore,　the　optimization　model　is　translated　into　a　quadratic　program.　Finally,　the　dual　sequence　quadratic　programming　(DSQP)　algorithm　and　the　global　convergence　method　of　moving　asymptotes　algorithm　with　two　different　filter　functions　(CEF　and　PF)　are　applied　to　solve　the　optimal　model.　Three　numerical　results　show　that　DSQP&CEF　has　the　best　performance　in　the　view　of　structural　mass　and　discretion.