A refrigerant compressor having a drive shaft rotatable to cause compression of a refrigerant gas, and a drive power transmission unit for transmitting a drive power from an external drive power source to the drive shaft, the drive power transmission unit having a pulley freely rotatably mounted around the drive shaft, a power transmitting element fixed to the drive shaft, and a shock absorbent rubber element arranged between the pulley and the power transmitting element for providing a positive engagement between the rubber element and the pulley, and between the rubber element and the power transmitting element. The shock absorbent rubber element absorbs a change in a load torque applied to the compressor before the torque change is transmitted to the external drive power source via the pulley, and disengages from at least one of the pulley and the power transmitting element when an excessive load torque is applied to the compressor to interrupt transmission of the excessive load torque from the compressor to the external drive power source.