  We consider edge effects in grafted polymer layers under compression. For a
semi-infinite brush, the penetration depth of edge effects $\xi\propto
h_0(h_0/h)^{1/2}$ is larger than the natural height $h_0$ and the actual height
$h$. For a brush of finite lateral size $S$ (width of a stripe or radius of a
disk), the lateral extension $u_S$ of the border chains follows the scaling law
$u_S = \xi \phi (S/\xi)$. The scaling function $\phi (x)$ is estimated within
the framework of a local Flory theory for stripe-shaped grafting surfaces. For
small $x$, $\phi (x)$ decays as a power law in agreement with simple arguments.
The effective line tension and the variation with compression height of the
force applied on the brush are also calculated.
