This study is aimed at representing efficient buckling analysis method by analyzing the buckling behavior and the buckling pressure of filament-wound cylindrical shell. First, finite element analysis was conducted to find the buckling pressure and the buckling behavior on the stacking angles of $[{pm}30/90]_{FW}$, $[{pm}45/90]_{FW}$ and $[{pm}60/90]_{FW}$. The buckling formula (ASME 2007, NASA SP-8007) was employed to find the buckling pressure. These results were compared and verified through hydrostatic pressure buckling experiments. Second, the values of buckling formula and buckling pressure values of finite element analysis were compared, while the stacking angle was made to change by 5 degrees from 20 to 70 degrees. According to the conducted finite element analysis, stacking property showed the safety factor of about 1.0 at the buckling pressure values of such filament-wound stacking angles as $[{pm}30/90]_{FW}$, $[{pm}45/90]_{FW}$ and $[{pm}60/90]_{FW}$. ASME 2007 buckling formula showed the safety factor ranging from 1.84 to 2.76. On comparison, the values of the NASA SP-8007 formula showed relatively low safety factors ranging from 1.2 to 1.45. When it comes to the result to which various stacking angles from 20 to 70 degrees were applied, the values to which an equivalent material property was applied showed safety factors ranging from 0.8 to 0.97 while the ASME 2007 and the NASA SP-8007 buckling formula values showed safety factors ranging from 1.7 to 2.9 and 0.8 to 1.4 respectively. Based on the result above, the ASME 2007 formula, a simplified version of the NASA SP-8007 formula is regarded as a buckling formula in which more reliable safety factors are considered.