The longitudinal vibration response of a simplified model of a vibration isolation module used in an underwater towed acoustic sensor array is estimated by finite element method and validated by impact resonance tests using a lumped mass system. The viscoelastic properties of the Kevlar-29 fabric strength member of the vibration isolation module are determined from transient tensile tests at different preloads and strain rates based on a five-parameter discrete viscoelastic model. Close agreement between finite element estimates and experimental results are obtained when strain rates of the strength member during viscoelastic parameter estimation tests and impact tests are matched.