The initial deflections exist between frames for the stiffend cylinders fabricated by welding. In this paper the influence of the initial deflection to the elastic behavior of a cylinder subjected to external hydrostatic pressure was studied using the mathematical expressions for the intial deflections as follows (1) w _{i 1}=δ (1-4ξ²) (2) w _{i 2}=δ/ w _ξ=0- w _ξ=1/2 ( w - w _ξ=1/2) (3) w _{i 3}= A sinh _κ2ξ sin _κ1ξ+ D cosh _κ2ξ cos _κ1ξ+k A theoretical analysis indicates that the influences of initial deflections are different by its forms. The pressures at which the total stress on the surface of the cylinder with initial deflection w _{i 3} equal to the yielding stress of material were calculated for the cylinders having diffrent dimentions. Results of these calculations are shown Fig. 4, which are nondimentional plots of ψ= qa/Yh versus ν²= b²/ah .