A new numerical approach is presented for predicting adhesion forces of particles at flat and rough surfaces. The new hybrid method uses the finite element method (FEM) for the determination of elastic and plastic particle deformation combined with numerical Hamaker summation. In the numerical approach, the influence of the plastic deformation can be fully included. We show how the adhesion force depends on the contact geometry and the material properties. For easy comparison with other models, the force-displacement behavior of the systems is presented. The numerical approach is supported by atomic force microscopy (AFM) measurements. The experimentally observed adhesion force hysteresis is described very well by the new approach. Although calculations in this article are focused on spherical particles, our approach can be extended to particles of arbitrary shapes.