The use of patterned covariance matrices in forming pedigree-based mixed models for quantitative traits is discussed. It is suggested that patterned covariance matrix models provide intuitive, theoretically appealing, and flexible genetic modeling devices for pedigree data. It is suggested further that the very great computational burden assumed in the implementation of covariance matrix-dependent mixed models can be overcome through the use of recent architectural breakthroughs in computing machinery. A brief and nontechnical overview of these architectures is offered, as are numerical and timing studies on various aspects of their use in evaluating mixed models. As the kinds of computers discussed in this paper are becoming more prevalent and easier to access and use, it is emphasized that it behooves geneticists to consider their use to combat needless approximation and time constraints necessitated by smaller, scalar computation oriented, machines.