A radial plunger pump is provided which includes a motor housing having a motor mounted therein. A pump housing is further provided and has a pump portion defined therein. A shaft is mounted between the motor and the pump portion so that the pump portion operates when rotation of the motor is transmitted to the pump portion by rotation of the shaft. A constant pressure chamber is defined between a first seal member and a second seal member both of which are fixed to the pump housing. The leakage of oil from the pump housing toward the motor housing is prevented by the first and second seal members and the constant pressure chamber. Further, a plate is provided within the constant pressure chamber which rotates with the shaft and prevents the entry of foreign objects into the constant pressure chamber through a constant pressure port which communicates to the ambient atmosphere.