The contact mechanics of a fibrillar micro-fabricated surface structure made of poly(dimethyl siloxane) (PDMS) is studied. The attachment and detachment of individual fibrils to and from a spherical indenter upon approach and retraction are detected as jumps in force and stiffness. A quantitative model describes the stiffness values by taking into account the deformation of the fibrils and the backing layer. The results emphasize the importance of long-range interactions in the contact mechanics of elastic materials and confirm some of the important concepts underlying the development of fibrillar adhesive materials.