This　paper　presents　the　nonlinear　chaotic　mechanical　model　for　magneto-electric　elastic　(MEE)　laminated　nanoplates,　with　the　flexomagnetoelectric　(FME)　effect,　subjected　to　multi-physical　field　excitation.　Utilizing　the　high-order　shear　deformation　theory　(HSDT),　Hamilton’s　principle,　and　the　nonlinear　strain-displacement　relationships　from　von　Karman’s　theory,　the　governing　nonlinear　equations　for　the　system　are　derived.　The　application　of　the　nonlocal　strain　gradient　theory　(NSGT)　facilitates　the　consideration　of　the　size　effect　in　the　system.　The　employment　of　the　Airy　stress　function　manages　the　nonlinear-nonlocal　terms　in　the　control　equation.　The　accurate　solution　approach　is　ultimately　formulated　by　combining　the　dual-mode　Galerkin　method　with　the　fourth-order　Runge-Kutta　method.　The　outcomes　indicate　that　the　nonlinear　chaotic　behavior　of　MEE　laminated　nanoplates　is　substantially　affected　by　the　FME　effect,　hygrothermal　conditions,　and　electromagnetic　field.　The　research　conducted　in　this　paper　intends　to　offer　the　comprehensive　theoretical　basis　for　the　utilization　of　MEE　nanomaterials　in　industrial　engineering,　alongside　the　derivation　of　criteria　essential　for　mitigating　and　controlling　the　nonlinear　chaotic　behaviors　within　the　system.　©　The　Author(s)　2025.