The analytic element method currently uses points, lines, polygons, circles, ellipses, and curvilinear line elements to represent features in models. A new set of elements with shapes that are more general than the ellipse have been created. The elements shape is that of an equipotential around a two-legged slot. Conformal mapping was used to map the boundary of the element onto the unit circle where groundwater flow problems were solved. The inverse mapping was performed by representing the mapping function with a set of series expansions and inverting the series. Models of multiple arbitrary shaped lakes have been created. Additional shapes to represent other features such as impermeable boundaries have also been created. These new shapes allow the modeling of features that are not circular or elliptical, and can represent shapes created using a set of curvilinear line elements, with a single element.