A mud pump is a reciprocating piston/plunger device designed to circulate drilling fluid

Drilling fluid

In geotechnical engineering, drilling fluid is a fluid used to aid the drilling of boreholes into the earth. Often used while drilling oil and natural gas wells and on exploration drilling rigs, drilling fluids are also used for much simpler boreholes, such as water wells. Liquid drilling fluid...

 under high pressure (up to 7500 psi (51,710,679.7 Pa) ) down the drill string

Drill string

A drill string on a drilling rig is a column, or string, of drill pipe that transmits drilling fluid and torque to the drill bit. The term is loosely applied as the assembled collection of the drill pipe, drill collars, tools and drill bit...

 and back up the annulus.

Mud pumps come in a variety of sizes and configurations but for the typical petroleum drilling rig

Drilling rig (petroleum)

This article lists the main components of a petroleum onshore drilling rig.Offshore drilling rigs have similar elements, but are configured with a number of different drilling systems to suit drilling in the marine environment....

, 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 Duplex mud pumps (two piston/plungers) have generally been replaced by the triplex pump, but are still common in developing countries.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 is 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 MWD and LWD retrieval.

The "normal" mud pump consist of two main sub-assemblies, the fluid end and the power end.

The fluid end produces the pumping process with valves, pistons, and liners. Because these components are high-wear items, modern pumps are designed to allow quick replacement of these parts.

To reduce severe vibration caused by the pumping process, these pumps incorporate both a suction and discharge pulsation dampener. These are connected to the inlet and outlet of the fluid end.

The power end converts the rotation of the drive shaft to the reciprocating motion of the pistons.
In most cases a crosshead crank gear is used for this.

Parts of mud pump:
1.housing itself.
2.liner with packing.
3.cover plus packing.
4.piston and piston rod.
5.suction valve and discharge valve with their seats.
6.stuffing box (only in double-acting pumps).
7.gland (only in double-acting pumps).