This book studies mantle distribution and crust dimpling and buckling of rotating Earth.Using mathematics and mechanics Principle of Minimum Potential Energy (PMPE) optimum theory etc we got some new results including : mantle distribution; spherical crust dimpling and buckling; special points (belt on 35 degree of south and north latitude) where the (PE) reaches optimum and should be noted. For example Tibet - high - land raising up and Earthquake happening.