A study result of buckling reliability is presented for the axially compressed imperfect elastic cylinder. Multi-mode analysis program is developed from Karman-Donnell Equation for the calculation of the buckling load of the cylindrical she1l. Geometric intial imperfection is approximated by double Fourier series of which coefficients are assumed random variables with jointly normal distribution characteristics. Crude Monte Carlo simulation technique is used to calculate the probabilistic failure properties of several cases with various imperfection Conditions.