The optical replication process and its advantages and disadvantages are reviewed. Substrate dimensional stability under normal exposure to thermal and dynamic stresses is identified as an important issue in the design and stability of replicas and the selection of materials for their fabrication. An analysis is presented to help in the selection of materials that are of particular interest in the construction of surfaces with low dynamic deflection. Typical manifestations of loss of dimensional stability for some of these materials are described. Data are presented for materials and methods of processing that were found to be particularly successful in overcoming problems of dimensional stability.