In this paper, the coefficient of the price index in the financial system is modified from a fixed constant to an elastic coefficient. Based on the RouthHurwitz theorem and the bifurcation theorem, the effect of the elastic coefficient on the stability of equilibrium points, pitchfork bifurcation, Hopf bifurcation and the chaos of the modified finance system are discussed. Moreover, numerical simulations by Matlab are used to test the obtained theoretical results. In addition, by means of numerical simulations, a change figure of the interest rate amplitude and the corresponding phase planes with parameter variations for the financial system are obtained and investigated. It visually exhibits the stability state, the periodic state and the chaos state of the financial system.