The purpose of this paper was to investigate the nonlinear elastic and inelastic behaviors of fixed parabolic arch ribs, due to the lack of study on fixed parabolic arch ribs. The in-plane nonlinear elastic and inelastic buckling behaviors and the strength of fixed parabolic arch ribs, when subjected to a vertically distributed load, were investigated using a finite element analysis. The FE models used in this study were verified using the results obtained by other researchers. The verification showed that the FE model used for the analysis was able to depict, with a good degree of accuracy, the in-plane behaviors of parabolic arch ribs. 75 FE models were used to investigate the nonlinear elastic behavior of a fixed parabolic arch subjected to a vertically distributed load. From the nonlinear elastic analysis, the buckling mode of arch ribs was observed to be dependent on the rise-span-ratio and S/r ratio of the arch ribs. 107 FE models, including residual stresses and initial imperfections, were analyzed to observe the inelastic behavior of fixed parabolic arch ribs. The effects of residual stresses and initial imperfections were investigated. Finally, it was found that the buckling curve for a straight column can be apply to fixed parabolic arch ribs subjected to a vertically distributed load with the exception of shallow arch ribs.