This paper describes the two-sided Jacobi-Davidson (TSJD) method to compute the critical modes of large scale power systems. For the proposed method

the selection strategy of eigenvalues is flexible. It converges to right and left eigenvectors as well as eigenvalues which can be used directly for modes analysis. The flow of TSJD method is described and we also give measures to improve computing efficiency. TSJD method is applied to power system state matrices with orders of 2940 and 29548. The results show that TSJD is reliable and efficient. It can be used to compute critical modes of practical large scale power systems.