The stability and chaotic vibrations of a pipe conveying fluid with both ends fixed, excited by the harmonic motion of its supporting base in a direction normal to the pipe span, were investigated with the aid of modern numerical techniques, involving the phase portrait, Lyapunov exponent and Poincare map etc. The nonlinear differential equations of motion of the system were derived by considering the additional axial force due to the lateral motion of the pipe. Attention was concentrated on the effect of forcing frequency and flow velocity on the dynamics of the system. It is shown that chaotic motions can occur in this system in a certain region of parameter space, and it is also found that three types of routes to chaos exist in the system: (i)period-doubling bifurcations; (ii)quasi-periodic motions; and (iii)intermittent chaos.