Based　on　Hamilton’s　principle,　a　general　three-dimensional　mechanical　model　with　consideration　of　the　consistent　couple　stress　theory　is　established　in　this　paper,　and　the　dynamic　governing　equations　and　boundary　conditions　are　derived　strictly.　After　that,　inspired　by　the　high-frequency　theory　established　by　Mindlin,　a　novel　two-dimensional　theory　of　micro-plates　is　proposed.　Governing　equations　and　boundary　conditions　are　simplified　and　further　validated　via　some　reductions　and　comparisons　with　the　traditional　Mindlin　plate　and　the　Timoshenko　beam.　As　an　application,　the　propagation　property　of　straight-crested　waves　in　a　micro-plate　is　investigated,　and　the　effect　of　couple　stress　is　revealed.　Then,　the　static　bending　and　free　vibration　of　a　simply　supported　rectangular　micro-plate　is　investigated　with　the　aid　of　the　double　Fourier　series.　It　is　demonstrated　that　the　couple　stress　has　significant　influence　on　the　mechanical　behaviors,　including　the　static　deflection　and　natural　frequency,　as　the　plate　thickness　shrinks.　Physically,　the　couple　stress　effect　is　equivalent　to　an　increase　in　structural　stiffness.　In　order　to　illustrate　the　effect　of　the　couple　stress,　a　general　criterion　for　quantifying　the　critical　size　that　distinguishes　microscale　from　macroscale　is　proposed　numerically.　To　some　extent,　it　can　also　be　viewed　as　a　criterion　for　distinguishing　the　consistent　couple　stress　theory　of　micro-structures　from　the　classical　continuum　mechanics　theory　of　macro-structures.　©　2020,　Springer-Verlag　GmbH　Austria,　part　of　Springer　Nature.