For a pure homogeneous deformation, suppose that are the lengths in the deformed state of linear elements parallel to the axes  and  respectively which have unit lengths in the undeformed state. Then by making  successively  and , we see that

and
and	(22.10)

Simple extension:
Consider the simple extension along x axis of a, incompressible neo-Hookean material for whom the stress-strain relations take the form:

	(22.11)

Since , we have  and  which gives,

(22.22)

Simple shear:

i.e .
and	(22..13)

Thus shearing stresses alone can not maintain a state of simple shear in the material. If the stresses and  are zero, then the stresses ; and if, then. Thus two possible stress systems which can maintain a simple shear:
(i) A shearing stress in the plane together with a normal stress parallel to the axis.
(ii) A shearing stress in the plane together with two normal stresses of magnitude parallel to the and  axes.