This paper is a critique of major weaknesses of current techniques for analyzing the reliability of computer communication networks. Several of the most important factors influencing the reliability seen by users of such systems have been almost completely ignored or modeled in a rudimentary fashion. Ignoring such factors may be partially justified by the inherent complexity of the problems being studied, which often precludes exact computations being feasible for networks of any size, even with simplifying assumptions. Nevertheless, the results of models which ignore such factors are questionable even if they are computable. The focus of models of such networks should be on the effects of system malfunctions, degraded performance, excessive delays, etc., on system users. New approximate modeling techniques appear to be the most realistic approach to studying such problems.