  We review some pseudo-planar deformations for the equations of incompressible
isotropic nonlinear elasticity first introduced in 1985 by Rajagopal and
Wineman. We extend this class of deformations to compressible isotropic and
transverse isotropic materials, and also consider the influence of gravity. We
consider some new approximate solutions and we discuss the possible relevance
of such solutions to the understanding of the complex structure of the fields
equations of nonlinear elasticity, using weakly nonlinear theories.
