The dynamic of nonlinear viscoelastic shallow arches subjected to the external excitation was investigated. Based on the d’Alembert principle and the EulerBernoulli assumption, the governing equation of shallow arch was obtained, where the Kelvin model was used to express the constitutive relation of nonlinear viscoelastic material, and the equation was simplified by the Galerkin’s method for numerical analysis. Moreover, the effects of the viscoelastic material parameter, the rise and excitation on the nonlinear dynamic including system bifurcation and chaos of shallow arch were investigated. The results show that the nonlinear dynamic properties of the viscoelastic shallow arches were very complex, and the periodic motion, quasiperiodic motion and chaotic motion appeared alternately for certain condition.