It is shown that in the initial phase there are two basic types of similar folding of multi-layered structures, referred to here as folding of the first and second kind, depending on the prevalence of over-all flexure or shear. A simple theory brings to light the underlying mechanics and the controlling parameters which govern these two types of folding and the transition from one to the other. The dominant wave length obtained in folding of the second kind is the same as derived previously (Biot, 1961) assuming the incompetent layers to act as lubricants. In folding of the first kind the system behaves approximately as a single layer (Biot, 1957; 1961). The same theory solves at the same time the problem of folding of a single anisotropic layer.