Abstract The nonlinear dynamical characteristics of vertical fluid conveying pipe under the condition of commonly elastic supports at both ends and the excitation of pulsating fluid and harmonic motion of the base were studied by using the nonlinear analysis methods to find out systematical parameter conditions and the forerunner of chaos. Numerical results show that the system goes through the transitions from periodic motion and chaotic motion alternately with the increase of mean flowrate and mass ratio. Doubling bifurcation is the route leading to chaotic motion, and the inverse doubling bifurcation is its converse way to leave chaotic motion. The parameter conditions of chaotic motion and periodic motion are closely related with fluid flowrate and supporting elastic coefficients of piping system. The parametric range of chaotic motion becomes short with the increase of elastic supporting and restraining coefficients. That shows that the coefficients are good for controlling the chaotic motion.