Various contact mechanics theories have been developed in recent years. The most popular are the statistical asperity theories of the type of Greenwood and Williamson and Persson’s theory, which treats self affine rough surfaces. The latter theory includes roughness at all length scales as well as long range elastic interactions. However, it is exact only at full contact conditions, which are often met by rubbers but not by metals. With metals in mind, we here use Green’s function molecular dynamics (GFMD) simulations to assess the validity of Persson’s theory at small loads, therefore small contact areas. GFMD is a boundary-value method which allows for ultra fine discretization of rough surfaces since it is computationally very efficient, and treats interfacial contact using interatomic potentials. To date, the GFMD method was only used in 3-D for modelling the normal loading of rough elastic semi-infinite incompressible (Poisson's ratio = 0.5) solids. In this work we extend GFMD in order to model both normal and tangential loading of rough solids with finite height and generic elastic properties. GFMD is then used to numerically calculate the proportionality constant κ between the area of real contact ar and nominal pressure p for the contact between a compressible linear elastic solid and a rough rigid punch. The numerically calculated value of the proportionality constant k is then extrapolated to the thermodynamic, fractal and continuum (TFC) limit. Results are then compared with that of the other analytical models.