Although swash-plate type axial piston pumps have the merits of wide operating conditions and high efficiency, the characteristics of pressure pulsation and flow ripple which result in system noise generation are on-going problems. This research examined the analytic models of the dynamic oil pressure and flow characteristics in the pump. A new mathematical model which considered the pressure behaviors of each cylinder and discharge piping was developed to analyze the pump pressure and flow. This model also considered the leakages in the clearances which many researchers have ignored so far. Using the developed model, numerical calculations were implemented. The results showed that widely used simple model which considered only a single cylinder can not predict actual discrete flow dynamics and that fluid inertia effect has to be considered in the mathematical model. Several critical parameters were discussed such as port volume and discharge resistance on the assumption that the pipe length is not so long. The effect of leakages was studied on the final stage.