In some previous studies it has been discovered that, contrary to the theoretical prediction, adhesive contact between an elliptical indenter and an elastomer begins to detach at the minor axis of the indenter. This work studies the adhesive contact between an elastomer and flat elliptical indenters. In particular, the influence of the elastomer thickness and hard particles in the contact zone is investigated both experimentally and numerically. In the experiments, the indenter was first immersed and then pulled off elastic layers of different thicknesses, where it was observed that the nucleation point of detachment moves from the minor axis of the indenter to the major axis as the layers become thicker. Both BEM (Boundary Element Method) and FEM (Finite Element Method) simulations were performed for this series of experiments. The results of the BEM simulations support the results of the experiments and indicate a possible transient regime, where the contact starts to detach at the edges of the major axis and then switches to detachment from the edges of the minor axis. In contrast to the BEM, which was formulated based on the frictionless contact, the contact of the indenter and the elastic layer is modeled as completely bonded in the FEM. It was found that for thick layers, both simulation methods give the same results (detachment from major axis). For moderately thin layers the FEM favors the detachment from the minor axis of the ellipse. It is interesting that for thin layers, the results of the FEM show fingering instabilities during detachment. In the second series of experiments, hard sand particles of different sizes and shapes were scattered on the elastic layer. The elliptical indenter was then immersed in the elastic layer to different indentation depths and then pulled off, until complete contact loss. It is observed that the bigger the indentation depth, the larger the direct contact area between the indenter and the elastomer, and the more pronounced the adhesion component of the normal force during the pull-off phase. For this series of experiments BEM simulations were performed, which show similar qualitative behavior.