Most of the surfaces have roughness down to atomic scales. When two surfaces come into contact, the nature of the roughness determines the properties like friction and wear. Analysis of the rough surface contacts is always complicated by the interaction between the material size effects and the micro-geometry. Contact mechanics could be simplified by decoupling these two effects by magnifying the scale of roughness profile. Also, tailoring the roughness at different scale could show a way to control the friction and wear through surface micro-structure modifications. In this work, the mechanics of contact between a rigid, hard sphere and a surface with a well defined roughness profile is studied through experiments and finite element simulation. The well defined roughness profile is made up of a regular array of pyramidal asperities. This choice of this geometry was mainly dictated by the fabrication processes. The specimens were made out of an aluminium alloy (6351-T6) such that there could be a direct application of the results in controlling the tribological properties during aluminium forming. Experiments on the pyramidal aluminium surface is carried out in a 250 kN Universal Testing Machine (INSTRON 8502 system) using a depth sensing indentation setup. A strain gauge based load cell is used to measure the force of the indentation and a LVDT (Linear Variable Differential Transformer) is used to measure the penetration depth. The load and the displacement were continuously recorded using a data acquisition system. A 3-D finite element framework for studying the elastic-plastic contact of the rough surfaces has been developed with the commercial package (ABAQUS). Systematic studies of indentation were carried out in order to validate the simulations with the experimental observations. The simulation of indentation of flat surface is carried out using the implicit/standard (Backward Euler) procedure, whereas, the explicit finite element method (Forward Euler) is used for simulating rough surface indentation. It is found that the load versus displacement curves obtained from experiments match well with the finite element results (except for the error involved in determining the initial contact point). At indentation depths higher than a value that is determined mainly by the asperity height, the load-displacement characteristics are similar to that pertaining to indentation of a flat, smooth surface. From the finite element results, it is found that at this point, the elastic-plastic boundary is more or less hemispherical as in the case of smooth surface indentation. For certain geometries, it is found that there could exist an elastic island in the sub-surface surrounded by plastically deformed material. This could have interesting applications.