Because modern technology depends on reliable supplies of a wide variety of materials, and because of increasing concern about those supplies, a comprehensive methodology has been created to quantify the degree of criticality of the metals of the periodic table. In this paper, we apply this methodology to the elements of the geological copper family: Cu, As, Se, Ag, Te, and Au. These elements are technologically important, but show a substantial variation in different factors relating to their supply risk, vulnerability to supply restriction, and environmental implications. Assessments are made on corporate, national, and global levels for year 2008. Evaluations of each of the multiple indicators are presented and the results plotted in "criticality space", together with Monte Carlo simulation-derived "uncertainty cloud" estimates for each of the aggregated evaluations. For supply risk over both the medium term and long term, As is the highest risk of the six metals, with Se and Ag nearly as high. Gold has the most severe environmental implications ranking. Vulnerability to supply restriction (VSR) at the corporate level for an invented solar cell manufacturing firm shows Se, Te, and Cu as approximately equal, Cu has the highest VSR at the national level, and Cu and Au have the highest VSRs at the global level. Criticality vector magnitudes are greatest at the global level for As (and then Au and Ag) and at the national level for As and Au; at the corporate level, Se is highest with Te and Cu lower. An extension of this work, now in progress, will provide criticality estimates for several different development scenarios for the period 2010-2050.