  Finite element methods are used to study non-adhesive, frictionless contact
between elastic solids with self-affine surfaces. We find that the total
contact area rises linearly with load at small loads. The mean pressure in the
contact regions is independent of load and proportional to the rms slope of the
surface. The constant of proportionality is nearly independent of Poisson ratio
and roughness exponent and lies between previous analytic predictions. The
contact morphology is also analyzed. Connected contact regions have a fractal
area and perimeter. The probability of finding a cluster of area $a_c$ drops as
$a_c^{-\tau}$ where $\tau $ increases with decreasing roughness exponent. The
distribution of pressures shows an exponential tail that is also found in many
jammed systems. These results are contrasted to simpler models and experiment.
