The displacement of a liquid by a less viscous fluid in a porous medium or other small geometry often results in an interfacial instability that takes the form of ''fingers'' or ''tongues.'' Typically referred to as viscous fingering or the Saffman-Taylor instability, this instability has direct relevance to many industries. For example in oil recovery nearby water can enter the oil reservoir and hinder yields, while some enhanced oil recovery techniques use fluids to displace oil and become less effective as the instability appears. This instability is also detrimental to gas-assisted injection molding and some embossing processes, while it could produce desirable effects in some industries such as patterning thin polymer films. Unfortunately the majority of studies of the two-phase displacement problem introduce the displacing fluid at a constant flow rate as opposed to a constant pressure. In this thesis a finite liquid drop is displaced radially by a gas at constant pressure in a Hele-Shaw cell. A Hele-Shaw cell consists of two parallel plates with a gap spacing much smaller than the length and width, effectively producing a two-dimensional flow. The problem is investigated in three separate studies: the displacement of glycerol-water mixtures by air, the displacement of aqueous calcium hydroxide by carbon dioxide, and the displacement of mineral oil with dissolved polyisobutylene, a shear-thinning liquid, by air. Experimental videos are analyzed to track the expansion of the gas phase and the development of the instability, and a simple conservation of volume approach is used to estimate the residual film produced by the displacement. Finally a novel quantity is defined to justly compare very different instability regimes such as smooth pedal-like fingers (primarily a Newtonian effect) and fractal dendritic fingers (primarily a shear-thinning effect) in order to quantify the instability and its growth.