In the present study, numerical simulations of the three-dimensional axisymmetric flow in a poppet valve for oil hydraulics are conducted using the vortex method. The fluids are assumed to be inviscid and incompressible. The vibration of the poppet occurs in the axial direction because the poppet is supported by a spring and a dashpot. Pulsating flow rates from a swash plate piston pump are employed as a boundary condition for comparison with experimental results and sinusoidal flow rates are also used as a boundary condition to investigate the effects of the frequency and the amplitude of the flow rate on the valve lift and flow in the valve. The process of jet flow development, the fluctuations of the valve lift and the velocity distributions in the valve are investigated for the vibrating poppet.