In applications such as MEMS and NEMS devices, the adhesion force and contact load may be of the same order of magnitude and the static friction coefficient can be very large. Such large coefficient may result in unacceptable and possibly catastrophic adhesion, stiction, friction and wear. To obtain the static friction coefficient of contacting real surfaces without the assumption of an empirical coefficient value, numerical simulations of the contact load, tangential force, and adhesion force are preformed. The surfaces in dry contact are statistically modeled by a collection of spherical asperities with Gaussian height distribution. The asperity micro-contact model utilized in calculation (the ZMC model), considers the transition from elastic deformation to fully plastic flow of the contacting asperity. The force approach of the modified DMT model using the Lennard-Jones attractive potential is applied to characterize the intermolecular forces. The effect of the surface topography on the static friction coefficient is investigated for cases rough, intermediate, smooth, and very smooth, respectively. Results of the static friction coefficient versus the external force are presented for a wide range of plasticity index and surface energy, respectively. Compared with those obtained by the GW and CEB models, the ZMC model is more complete in calculating the static friction coefficient of rough surfaces.