In this paper we discuss passive vibration isolation systems for ultralow temperature gravitational radiation detectors, using a detector at Stanford University as the primary example. We review the basic theory of such isolation systems and describe methods of analysis for one‐degree‐of‐freedom isolators. With these methods we derive fundamental constraints on the performance of gravitationally loaded isolators. Next we discuss general design considerations, optimization, and detailed analysis of six‐degree‐of‐freedom isolators. We conclude with experimental data from isolators designed for the Stanford gravitational radiation detector.