The isophotes of elliptical galaxies frequently deviate from pure isophotes, typically taking a boxy or disky shape. I present two families of models for the intrinsic light distribution of elliptical galaxies; both families consist of a purely ellipsoidal light distribution with the addition of a secondary, nonellipsoidal light distribution which accounts for the isophotal distortion. In the first family of models, the nonellipsoidal distribution has isoluminosity surfaces in the shape of a box, or rectangular prism. These models may appear disky in projection (a4 > 0) from a limited range of viewing angles. Furthermore, the skew component of the isophotal distortion (b4) may be comparable in amplitude to the a4 component. In the second family of models, the nonellipsoidal distribution is cylindrical. In these models, the isophotal distortion is boxy (a4 < 0). For both families of models, if a fraction f = 0.16 of the total light is in the nonellipsoidal component, the resulting isophotal distortions are only at the 1% level.