Calculating the critical load that could lead to beam failure through buckling is a complex issue. This paper intends to analyze the stability of arches taking into account how the curvature, material properties, load positions and geometry affect the behavior. Unlike in many other articles, the impact of the bending moment on the membrane strain is also incorporated into the model. To derive the buckling equilibrium equation, the principle of virtual work is applied, and analytical solutions for the limit point buckling are provided. It is worth noting that the load location has a significant impact on the buckling load, and this relationship is strongly associated with the ratio of the arch length to the radius of the gyration of the structure. It is found that in the case of fixed arches, two stable equilibrium branches and one unstable branch can be observed when buckling is possible. When the load is positioned sufficiently far from the crown point, the load-carrying capacity of the structure improves.