The critical loads for flexural buckling of axially loaded fiber reinforced polymer (FRP) members were investigated. A test database containing data of axial compression tests of 176 FRP members that failed in the flexural buckling mode was established. Five existing models proposed by Euler, Engesser, Haringx, Strongwell company, and Fiberline company for predicting flexural buckling loads were summarized and evaluated. An equation to determine the stability factor for global buckling of FRP members under axial compression was developed based on the observed initial crookedness of FRP members. Then, a theoretical model of flexural buckling loads of FRP members was proposed considering the influence of initial crookedness of FRP members. On the basis of the proposed database, an empirical model of flexural buckling loads of FRP members was derived through regression analysis. The two models were verified by the test database and numerical simulations. Finally, the performance of the two proposed models was analyzed. Results show that by using the proposed test database (section width of members is between 25.4 mm and 254 mm, section height is between 25.4 mm and 254 mm, and effective length is between 203 mm and 6 300 mm), the error of the model proposed by Strongwell company was the highest, and models proposed by Euler, Engesser, and Haringx overestimated the flexural buckling loads of FRP members, while that proposed by Fiberline company underestimated the flexural buckling load. The proposed theoretical model and empirical model both obtained more accurate results than the comparison models in predicting axially loaded FRP members within the range of section dimension and effective length covered by the test database. The proposed models were applicable to axially loaded FRP members with I-shaped, L-shaped, square, and circular sections, and could accurately predict the flexural buckling loads of axially compressed FRP members within the above parameter range.