Abstract: The geometric buckling is of great value in application to criticality problem and analysis of dynamic process of supercritical system in fast fission reactor. The geometric buckling of bare reactor of homogeneous ellipsoid is solved analytically with variational method, and the deductive process is given in detail in this paper, We also apply the solution to bare reactor of inhomo-geneous ellipsoid and infinite reflected reactor. The analytical results agree quite well with the ones of 2 dimesion numerical simulation.