Abstract: The stiffened thin-walled structures are broadly used in the lightweight design of aerospace structures. With the increase in structure size and geometric characteristics, more refined meshes are needed to meet the requirements of analysis accuracy. The conventional isogeometric method adopts the topological structure in the form of NURBS tensor product, which makes it challenging to achieve local refinement in the analysis process, and global refinement will increase unnecessary degrees of freedom. In order to improve the accuracy and efficiency of numerical analysis of stiffened plate and shell structures, an adaptive isogeometric buckling analysis method based on RPHT-spline (rational polynomial splines over hierarchical T-meshes) for stiffened structures is presented in this paper. The spline mesh can be refined locally and adaptively along the stiffener paths, which effectively improves the accuracy of isogeometric buckling analysis of stiffened panels with low degrees of freedom. Firstly, the skins and stiffeners are modelled using RPHT-spline surfaces and NURBS curves, respectively. The geometric modeling and numerical simulation adopt a unified geometric language to achieve the integration of modelling and analysis. Secondly, the geometric projection algorithm and spline interpolation algorithm are used to achieve the high-efficiency and high-precision strong coupling between skins and stiffeners. In addition, an adaptive mesh refinement method driven by the stiffener paths is established. Finally, two numerical examples, a curve stiffened plate and a grid stiffened shell, verify the efficiency and robustness of the proposed method. Compared with NURBS-based isogeometric analysis, the proposed method can significantly reduce the total degrees of freedom of the analysis model.