Based　on　the　mathematical　similarity　of　the　axisymmetric　eigenvalue　problems　of　a　circular　plate　between　the　classical　plate　theory(CPT),　the　first-order　shear　deformation　plate　theory(FPT)　and　the　Reddy＇s　third-order　shear　deformation　plate　theory(RPT),　analytical　relations　between　the　eigenvalues　of　circular　plate　based　on　various　plate　theories　are　investigated.　In　the　present　paper,　the　eigenvalue　problem　is　transformed　to　solve　an　algebra　equation.　Analytical　relationships　that　are　expressed　explicitly　between　various　theories　are　presented.　Therefore,　from　these　relationships　one　can　easily　obtain　the　exact　RPT　and　FPT　solutions　of　critical　buckling　load　and　natural　frequency　for　a　circular　plate　with　CPT　solutions.　The　relationships　are　useful　for　engineering　application,　and　can　be　used　to　check　the　validity,　convergence　and　accuracy　of　numerical　results　for　the　eigenvalue　problem　of　plates.