A　size-dependent　Kirchhoff　micro-plate　model　resting　on　elastic　medium　is　developed　based　on　the　strain　gradient　elasticity　theory.　Three　material　length　scale　parameters　are　introduced　in　the　model,　and　those　parameters　may　effectively　capture　the　size　effect.　The　model　can　degenerate　into　the　modified　couple　stress　plate　model　or　the　classical　plate　model　by　setting　two　(l　(0)　and　l　(1))　or　all　(l　(0),　l　(1)　and　l　(2))　of　the　material　length　scale　parameters　to　be　zero.　Analytical　solutions　for　the　static　bending,　buckling　and　free　vibration　problems　of　a　rectangular　micro-plate　with　all　edges　simply　supported　are　obtained.　The　results　predicted　by　the　present　model　are　compared　with　those　predicted　by　the　degraded　models.　Influences　of　the　elastic　medium　on　the　static　bending,　buckling,　and　free　vibration　are　discussed.　The　results　show　that　the　present　model　can　predict　prominent　size-dependent　normalized　stiffness,　buckling　load,　and　natural　frequency　with　the　reduction　of　structural　size,　especially　when　the　plate　thickness　is　on　the　same　order　of　the　material　length　scale　parameter.　The　study　may　be　helpful　to　guide　the　design　of　microplate-based　devices　resting　on　elastic　medium　for　a　wide　range　of　potential　applications.