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Finite element methods are used to study non-adhesive, frictionless contactbetween elastic solids with self-affine surfaces. We find that the totalcontact area rises linearly with load at small loads. The mean pressure in thecontact regions is independent of load and proportional to the rms slope of thesurface. The constant of proportionality is nearly independent of Poisson ratioand roughness exponent and lies between previous analytic predictions. Thecontact morphology is also analyzed. Connected contact regions have a fractalarea and perimeter. The probability of finding a cluster of area $a_c$ drops as$a_c^{-\tau}$ where $\tau $ increases with decreasing roughness exponent. Thedistribution of pressures shows an exponential tail that is also found in manyjammed systems. These results are contrasted to simpler models and experiment.Comment: 13 pages, 15 figures. Replaced after changed in response to referee  comments. Final two figures change

Finite-element analysis of contact between elastic self-affine surfaces