According to the acting type

Mud pumps can be divided into single-acting pump and double-acting pump according to the completion times of the suction and drainage acting in one cycle of the piston's reciprocating motion.

According to the quantity of liners (piston/plunger)

Mud pumps come in a variety of sizes and configurations but for the typical petroleum drilling rig, the triplex (three piston/plunger) mud pump is the pump of choice. Duplex mud pumps (two piston/plungers) have generally been replaced by the triplex pump, but are still common in developing countries. Two later developments are the hex pump with six vertical pistons/plungers, and various quintuplex's with five horizontal piston/plungers. The advantages that these new pumps have over convention triplex pumps is a lower mud noise which assists with better Measurement while drilling (MWD) and Logging while drilling (LWD) decoding.