The hinged boom structures of crawler cranes are typical slender frame structures, whose stability is an important basis for lifting performance. The boom structures are divided into several substructures by taking each section as an element, and an embedded coordinate system is defined. Internal displacements of each substructure are reduced to the displacements of its boundary ends through the condensation of degrees of freedom. Based on the co-rotational method, the generalized nodal internal forces for substructure elements are formulated. Considering the mechanism constraints for the boom structures and the load lifting ways, the additional nodal external forces and their derivatives on the structure and mechanism displacements are obtained. The equations by differentiating the equilibrium equations of generalized nodal forces for the boom structures of crawler cranes with respect to the load factor are obtained. The critical load can be obtained through solving the differential equations and considering the instability criterion. A numerical example of hinged boom structures for a kind of crawler crane is given, which proves the presented method to be quick and high accuracy.