Abstract: The stability experiment of compression columns is important in material mechanics. This paper analyzes the stability of compression composite columns with rigid parts at both ends, based on the Euler method for the analysis of the stability of small disturbance elastic systems. The critical loads of the compression columns with different proportions of rigid parts are discussed through numerical solutions. Meanwhile, the results of the theoretical analysis are verified by the finite element numerical simulation. The results of this study will provide a guidance for the experiment teaching of the compression column stability.