For studying systems with a cubic anisotropy in interfacial energy σ, we extend the Cahn-Hilliard model by including in it a fourth rank term, which leads to an additional linear term in the evolution equation for the compositioneld. It also leads to an orientation-dependent effective fourth rank coeffcient γ(hkl) in the governing equation for the one-dimensional composition prole across a planar interface. The main effect of a non-negative γ(hkl) is to increase both σ and interfacial width w, each of which, upon suitable scaling, is related to γ(hkl) through a universal scaling function. The anisotropy in the interfacial energy can be large enough to give rise to corners in the Wul. shapes in two dimensions. In particles of finite sizes, the corners get rounded, and their shapes tend towards the Wul. shape with increasing particle size. In the study of unmixing of concentrated alloys, the anisotropy not only leads to non-spherical particle shapes, but also to strongly elongated morphologies.