According to the characteristic of poor stiffness of V-shaped beams, transverse dynamic instability model of V-shaped is presented by Catastrophe Theory. Mechanism of stability of V-shaped is analyzed. Coordinates of two cusps and instable bifurcation set is derived. Effect of nonlinear coefficient and frequency ratio on amplitude of V-shaped beams are analyzed. When nonlinear coefficient is , continuous change of can arise abrupt change of amplitude. Then the jumping phenomenon can leads destruction of V-shaped beams.