Mosquitoes drink using a pair of in-line muscular pumps in the head that draw liquid food through a long drinking channel termed as proboscis. Experimental investigations of mosquito drinking using synchrotron x-ray indicate two modes of drinking, a predominantly occurring continuous mode in which the anterior cibarial and posterior pharyngeal pumps expand cyclically at a constant phase difference and an isolated burst mode in which the pharyngeal pump expansion is several orders of magnitude larger than in the continuous mode. The objective of this thesis is to explain the mechanics and functional implication of this two-pump dual mode drinking of a mosquito. A reduced order mathematical model suggests that the primary role of the pharyngeal pump is in the burst mode. Since the precise geometry of the pump during drinking is yet not known, the drinking mechanism is modeled using different pump geometries based on morphological constraints in the animal. The model shows the continuous mode as being more effective in terms of energy expenditure, while the burst mode creates a large pressure difference across the proboscis which might be used to clear an obstruction in the channel or prime the channel. The hypothesis regarding the ability of a mosquito to self-clear an obstruction is analyzed by modeling the presence of an air bubble inside the system. The model indicates that air bubbles maybe able to stop flow during continuous mode drinking, and these same bubbles can be cleared by switching temporarily to burst mode drinking.