Abstract: In terms of the elastic stability of compressed flanges in a steel box girder and a thin-walled concrete box girder, an analytical approach that can be used for the elastic buckling analysis of continuous rectangular thin plates with multi-span elastic supports is proposed, based on the state-space method. The proposed method is verified by comparing with the results from the finite strip method. By the proposed method, this paper investigates the following parameters that influence the elastic buckling, including the stiffness of the elastic supports, the arrangement of the position and spacing of the elastic supports, and the in-plane compressive load conditions. The results demonstrate that the elastic supports have a significant influence on the elastic buckling of a continuous plate, and the buckling coefficient increases non-linearly as the support stiffness increases. Elastic supports with equal spacing and equal stiffness are beneficial to the stability of a continuous plate, while the significant difference of the support stiffness or the support spacing will result in obvious unfavorableness to the stability of the continuous plate, and the larger difference the more unfavorable. Under different loading cases, the varying tendency of the correlative curves of stiffness versus buckling coefficients is almost same. When the support stiffness is small, load parameters have a significant effect on a buckling coefficient. The buckling coefficient of a continuous plate subjected to a uniaxial in-plane compressive load is almost two times of that subjected to a biaxial in-plane compressive load.