A variety in mathematics is the solution set of a system of polynomial equations. These polynomials can be in any number of variables and, when graphed, form curves, surfaces, or hypersurfaces in n-dimentional space. If we could see in n dimensions, then we would define singular points to be those on this graph that come at irregularities (self-intersections or cusps, for example). The singular locus is the set of singular points in a given variety. In this project, we analyze the formal definition of a singular point and work towards finding an algorithm which will compute the singular locus.