The causes of low back pain associated with prolonged exposure to whole-body vibration are not understood. An understanding of non-linearities in the biomechanical responses is required to identify the mechanisms responsible for the dynamic characteristics of the body, to allow for the non-linearities when predicting the influence of seating dynamics, and to predict the adverse effects caused by various magnitudes of vibration. Twelve subjects were exposed to six magnitudes, 0.25–2.5 m s⁻² rms, of vertical random vibration in the frequency range 0.2–20 Hz. The apparent masses of the subjects were determined together with transmissibilities measured from the seat to various locations on the body surface:​ the upper and lower abdominal wall, at L3, over the posterior superior iliac spine and the iliac crest. There were significant reductions in resonance frequencies for both the apparent mass and the transmissibilities to the lower abdomen with increases in vibration magnitude. The apparent mass resonance frequency reduced from 5.4–4.2 Hz as the magnitude of the vibration increased from 0.25–2.5 m s⁻² rms. Vertical motion of the lumbar spine and pelvis showed resonances at about 4 Hz and between 8 and 10 Hz. When exposed to vertical vibration, the human body shows appreciable non-linearities in its biodynamic responses. Biodynamic models should be developed to reflect the non-linearity.