The present paper discusses on elastic buckling load and ultimate strength of reticulated cylindrical roofs under uniform lateral loads in the case of two boundary conditions of simple support and pin support. First, classical buckling load under a uniform lateral load is newly derived mathematically based on a simple approximation, followed by comparison with the linear elastic buckling loads calculated using FEM analysis. The comparison is performed to find approximate relations between the classical buckling loads and the FEM linear buckling loads for simple support and pin support. Second, elastic buckling loads are investigated based on FEM analysis considering geometrical imperfections, followed by derivation of formula for imperfection sensitivity which enables engineers to evaluate elastic buckling loads with hand calculation. Third, elastic plastic buckling loads are investigated based on FEM analysis also considering geometric imperfection, and the imperfection sensitivity of elastic plastic buckling loads is formulated mathematically. Finally, an estimation procedure for elastic plastic buckling loads is proposed based on the elastic buckling loads and the imperfection sensitivity for elastic plastic buckling loads in the two cases of boundary conditions.