The problem on the elastoplastic state of a thick isotropic plate (the case
of plane deformation) is solved. A larger prismatic inclusion is made a cl
ose fit in a polygonal hole in the plate. The plate is stretched at infinit
y by constant mutually perpendicular forces. The problem is solved by the s
mall-parameter method and by the theory of ideal plasticity. The axisymmetr
ic state of the plane with a circular hole stiffened by a round ring with a
constant force applied to its inner contour is considered as a zero approx
imation. Some specific shapes of the hole and reinforcing elastic rigid rin
g are considered.