Geckos have a unique ability to cling to ceilings and walls utilizing dry adhesion. Their foot pads are covered by a large number of small hairs (setae) that contain many branches per seta with a lower level of spatulae. Their fibrillar structure is the primary source of high adhesion. In this study, we construct the adhesion design database for biomimetic adhesive system. A simple idealized fibrillar structure consisting of single array of beams is modeled. The fibers are assumed as oriented cylindrical cantilever beams with spherical tip. We consider three necessary conditions; buckling, fracture and sticking of fiber structure, which constrain the allowed geometry. The adhesion analysis is performed for the attachment system in contact with rough surfaces with different s values for different main design variables-fiber radius, aspect ratio and material elastic modulus and so on. The developed adhesion design databases are useful for understanding biological systems and for guiding of fabrication of the biomimetic attachment system.