The advent or high-strength steel has enabled the arch structures to be relatively light, durable and long-spanned by reducing the cross sectional area. On the other hand, the possibility of collapse may be increased due to the slender members which may cause the stability problems. The limit analysis to estimate the ultimate load is based on the concept of collapse mechanism that forms the plastic zone through the full transverse sections. So, it is not appropriate to apply it directly to the instability analysis of arch structures that are composed with compressive members. The objective of this study is to evaluate the ultimate load carrying capacity of the parabolic arch by using the elasto-plastic finite element model. As the rise to span ratio (h/L) varies from 0.0 to 0.5 with the increment of 0.05, the ultimate load has been calculated fur arch structures subjected to uniformly distributed vertical loads. Also, the disco-elasto-plastic analysis has been carried out to find the duration time until the behavior of arch begins to show the stable state when the estimated ultimate load is applied. It may be noted that the maximum ultimate lead of the parabolic arch occurs at h/L=0.2, and the appropriate ratio can be recommended between 0.2 and 0.3. Moreover, it is shown that the circular arch may be more suitable when the h/L ratio is less than 0.2, however, the parabolic arch can be suggested when the h/L ratio is greater than 0.3. The ultimate load carrying capacity of parabolic arch can be estimated by the well-known formula of kEI/L$^3$where the values of k have been reported in this study. In addition, there is no general tendency to obtain the duration time of arch structures subjected to the ultimate load in order to reach the steady state. Merely, it is observed that the duration time is the shortest when the h/L ratio is 0.1, and the longest when the h/L ratio is 0.2.