Surge pressure is supplemental pressure because of the movement of the pipes downward and the swab pressure is the pressure reduction as a result of the drill string's upward movement. Bottom hole pressure is reduced because of swabbing influence. An Investigation showed that the surge pressure has great importance for the circulation loss problem produced by unstable processes in the management pressure drilling (MPD) actions. Through Trip Margin there is an increase in the hydrostatic pressure of mud that compensates for the reduction of bottom pressure due to stop pumping and/or swabbing effect while pulling the pipe out of the hole. This overview shows suggested mathematical/numerical models for simulating surge pressure problems inside the wellbore with adjustable cross-section parts. The developed models require simple input data that may be gotten from the rig location. Pressure variations due to Swabs and surge has been a major concern in the oil industry for numerous years. If the pressure variations become moreover extraordinary, this leads to formation fracture, and formation influx principal to a kick. In the worst circumstances and situations that kick principal on the blowout and put crew life in hazard. By using theoretical investigation and experimental consequences, it established that the surge pressure is a function of the well depth, the drilling tools combination, the diameter of the wellbore, drilling mud properties, drilling pipe operation speed, and acceleration of the drill pipe movement, etc. This review focuses and investigates the essential theory and on software that computes the pressure variations in different flow conditions to predict surge and swab pressure values.