Multiple‐stage seismic vibration isolation stacks, which consist of alternating layers of stiff masses and compliant springs, can provide significant passive filtering of ground vibration for experiments and equipment that are sensitive to mechanical noise. We describe the design, modeling and testing of a prototype of a stack suitable for use in the Laser Interferometer Gravitational‐wave Observatory (LIGO). This is a four‐stage elastomer (spring) and stainless steel (mass) stack, consisting of a table resting on three separate legs of three layers each. The viscoelastic properties of elastomer springs are exploited to damp the stack’s normal modes while providing rapid roll‐off of stack transmission above these modal frequencies. The stack’s transmission of base motion to top motion was measured in vacuum and compared with three‐dimensional finite‐element models. In one tested configuration, at 100 Hz, horizontal transmission was 10−7, vertical transmission was 3×10−6, and the cross‐coupling terms were between these values. ©1996 American Institute of Physics.