We describe the deformation behavior of polymer brushes and mushrooms compressed by finite-sized particles for the cases where the chains are fixed or mobile on the grafting surface. When the size of the particle is large compared to the grafting distance of the chains, the force on the particle is the same to lowest order in compression for both the fixed and surface mobile chains. Compression of a single mushroom can lead to a first order like escape transition, where part of the chain escapes from under the particle. These transitions can be seen either in the chain radius or in the compressional force law behavior. For surface mobile mushrooms, the force is considerably smaller because of the evacuation of chains from under the particle. The force law in this case also exhibits a maximum at a certain compression, indicating that the system undergoes a collapse transition above a critical pressure or yield stress P-c approximate to kT sigma(0)R(F3)(-1), where sigma(0) is the grafting density (chains/area) and R(F3) is the unperturbed mushroom size. Finally; we consider the case of bending of stiff chains grafted to a solid surface. In the case of a single chain, the force is a constant for weak compressions. In the multichain case, the force can be substantially lower because of the escape of chains from under the particle.