Although the stress of oscillatory shear flow can be decomposed into elastic and viscous parts in the linear regime, it is not yet known how to decompose the stress of a large amplitude oscillatory shear (LAOS) flow. We developed a method of analyzing LAOS data, which decomposes the stress into elastic and viscous components on the basis of a sound mathematical and physical foundation. This method is based on the symmetry of the stress and is a generalization of linear viscoelasticity from the viewpoint of geometry. The proposed method is more powerful than previous methods such as Fourier transform analysis and the Lissajous plot, in that it is more sensitive to the presence of nonlinearities and it is easier to determine nonlinear parameters. (C) 2005 The Society of Rheology.