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Buckling collapse and its analytical method of steel reticulated domes with semi-rigid ball joints are discussed, on the basis of a nonlinear elastic–plastic hinge analysis formulated for three-dimensional beam-columns with elastic perfectly plastic hinges located at both ends and the mid-span for each member. The second-order elastic analysis for reticulated domes, composed of members with semi-rigid connections modelled with elastic springs at the member ends, in conjunction with an update Lagrangian formulation, is carried out. Reductions in collapse loads due to semi-rigidity of the connections, as well as to the geometric imperfections of nodal coordinates and member crookedness, are investigated. The reductions of member strength are also plotted and summarized as the function of generalized slenderness, on the basis of which, the axial strength in the member is expressed ready for use to estimate the collapse loads of reticulated domes.