A theoretical studies are presented for the some problems of shell instability of circular cylindlrical shells subjected to hydrostatic pressure. The method used is that of minimumization of the total potential. (1) Effect of frame on shell buckling The deformation of the shell immediately befor buckling was assumed to be uniform by previous investigators. But the deflection prior to buckling is not uniform owing to the effect of the frame on the deflection, it is the axisymmetrical deformation. The buckling pressure occured from this axisymmetrical state is calculated. (2) Effect of buckling configulation An axitial distribution of radial displacement during buckling was given by Q =cosπξ in many previous papers. But it may be thought that buckled wave pattern is more flat form than cosπξ by the effect of tangential stress existing in the shell, then the buckling pressure obtained by putting the buckled wave pattern as follows Q = A sinh κ₂ξ sin κ₁ξ+ D cosh κ₂ξcos κ₁+ K is compared to the pressure in the case of the pattern given by cosπξ. (3) Error of approximate formula of buckling pressure The approximate formulas of buckling pressure developped from Mieses' accurate formula by Tokugawa or Windenburg are used generally for the disign and checking of experimental data. The accuracies of these formulas are examined, and checking of experimental data by Mieses' formula are proposed.