A new method for simulating dry contacts of three-dimensional rough surfaces has been developed. The present work is based upon Moving Grid Method (MGM) which greatly reduces the required computer memory size. One of the major difficulties in simulating contact problems is the huge requirement in computer Random Access Memory (RAM). The total number of nodes (N) to represent a typical three dimensional roughness topography can easily be in the order of tens of thousands. To store the corresponding deformation matrix based on conventional matrix method requires memory size in the order of N2. The computational time necessary to construct such a matrix is also proportional to N2. Thus a reasonable solution for the three dimensional contact problem can be difficult to obtain. In Moving Grid Method, the required storage space for the deformation matrix is reduced to the order of N. The computing time to construct the matrix is also proportional to N. The contact simulation solutions which include the asperity pressure distributions and the corresponding deformed surface profiles were calculated. The digitized surface profiles were used in the simulations. The 3-D results were compared with an existing 2-D model and the comparison showed excellent agreement.