Longitudinal-cross geometrical non-linear waves of deformation

The author considers the task of constructing differential equations' characteristics and relations on them. The other task was to define the speed of propagation of longitudinal-cross deformation waves in continuum, mechanical behavior of which is described by arbitrary cross relations between the first invariants of tensors and second invariants of stress and deformation deviators. Conditions of the origin of purely longitudinal and pure cross-waves were researched. As an example, the vector diagrams of long cross-waves' deformation for three mathematical models of continuum are constructed.