For modelling purposes and for evaluation of driver's seat performance in the vertical direction various mechano-mathematical models of the seated human body have been developed and standardized by the ISO. No such models exist hitherto for human body sitting in an upright position in a cushioned seat upper part, used in industrial environment, where the fore-and-aft vibrations play an important role. The interaction with the steering wheel has to be taken into consideration, as well as, the position of the human body upper torso with respect to the cushioned seat back as observed in real driving conditions. This complex problem has to be simplified first to arrive at manageable simpler models, which still reflect the main problem features. In a laboratory study accelerations and forces in x-direction were measured at the seat base during whole-body vibration in the fore-and-aft direction (random signal in the frequency range between 0.3 and 30 Hz, vibration magnitudes 0.28, 0.96, and 2.03 ms(-2) unweighted rms). Thirteen male subjects with body masses between 62.2 and 103.6 kg were chosen for the tests. They sat on a cushioned driver seat with hands on a support and backrest contact in the lumbar region only. Based on these laboratory measurements a linear model of the system-seated human body and cushioned seat in the fore-and-aft direction has been developed. The model accounts for the reaction from the steering wheel. Model parameters have been identified for each subject-measured apparent mass values (modulus and phase). The developed model structure and the averaged parameters can be used for further bio-dynamical research in this field.