We present molecular dynamics simulations in which we determine the forces on cubes, rods, discs, and spheres that are included in polymer brushes at different distances from the anchoring surface. We show that one can predict the forces on such particles by combining multiple theoretical models that consider (1) the excluded volume interaction caused by the presence of a polymer cavity in the brush, (2) the surface tension due to the created particle polymer interface, and (3) a correction to the pressure gradient over the particle surface induced by a streamlining effect on the polymer paths. Our description of the distance-dependent inclusion free energy and force for spherical and nonspherical particles in polymer brushes might ultimately aid in the development of brush-based sensors and filters, which rely on enhancing or preventing the entrapment of arbitrarily shaped particles.