ppl in a plane stress problem, it is assumed that perpendicular to the plane shear stress and normal stress is zero.

but due to the strain in directions parallel to the plane , there must be a strain in the direction perpendicular to the plane by poisson's effect, which will cause a normal stress.

so is the assumption made as normal stresses @ surface is zero ( as surface is free of loads in one direction and hence there is no deformations possible in the elements on surface) and by omitting the stress in the interior

Regards

WOT