Recently, the authors have proposed a simulation method for predicting transient responses of fluid transmission lines (rigid and viscoelastic lines). The purpose of this study is to confirm the availability of a simulation method when it is applied to fluid lines connected to pumps. The fluid lines dealt with here are composed of flexible hoses (a fluid viscoelastic line) and rigid lines. As a method for simulating transient responses for fluid lines, we adopted a technique for formulating rational polynomial approximations for transfer matrix elements of fluid lines. In this study, each fluid line system connected to two kinds of pumps, consisting of a vane pump and axial piston pump, was investigated. The waveforms of the pressure pulsation induced in these systems are calculated using simulation. The results obtained are compared with the experimental results. It may be concluded that the simulation method adopted in this study can be useful for predicting the pressure pulsation induced in these systems.