In this talk, we are concerned with the similarity problem for the Cowen-Douglas class. The unitary equivalence counterpart was already investigated in the 1970s and geometric concepts including vector bundles and curvature appeared in the description. As the Cowen-Douglas conjecture shows, the study of the similarity problem has not been so successful until quite recently. The latest results reveal the close correlation between Model theorem, the corona problem, and the similarity problem for Cowen-Douglas operators. We give a sufficient condition for a Cowen-Douglas operator to be similar to the backward shift operator on a certain reproducing kernel Hilbert function space. Furthermore, from the perspective of weight sequences, we also present necessary condition for the different contractility of backward weighted shift operator tuples in different Model theorems.