This paper presents the Hencky bar-chain model (HBM) for the elastic in-plane buckling analysis of arches of any shape, support and loading conditions. The arches are assumed to be elastic, inextensible and have the same flexural rigidity EI throughout the entire length of the arch. Upon describing the Hencky bar-chain model, the strain energy of the deformed rotational elastic springs, potential energy of the axial force and the total potential energy functions are presented. By using the principle of minimum potential energy, the governing eigenvalue equation is derived. To illustrate the HBM, some arch buckling problems involving parabolic arches with different support conditions and carrying non-uniformly distributed load will be solved and their buckling loads compared with existing results if available.