The purpose of this study was to investigate the mechanical impedance of the human hand-arm system during exposure to random vibration under various experimental conditions and to evaluate statistically whether these experimental conditions have any influence on magnitude and phase of the mechanical impedance. A further aim was to compare the obtained results with other investigations where sinusoidal excitation has been used. The mechanical impedance was estimated in ten healthy subjects during exposure to random vibration, with a constant velocity spectrum within the frequency range 4–2000 Hz, by use of a specially designed laboratory handle. In the study, the influence of various conditions, such as vibration direction (X_h, Y_h, Z_h), grip force (25–75 N), feed force (20–60 N), frequency-weighted acceleration level (3, 6, 9, 12 m/s²) and hand and arm posture (five flexions, two abductions) were studied. The outcome showed that the vibration direction and the frequency of the vibration stimuli have a strong significant influence on the impedance of the hand. An increased vibration level resulted in a significantly lower impedance for frequencies over 100 Hz. Increased grip and feed forces led on the other hand to an increased impedance for all frequencies. With regard to hand and arm posture, the results show that the flexion and abduction had a significant contribution for frequencies below 30 Hz. Furthermore, the influence of some of the studied variables had a non-linear effect on the impedance but also differed between different exposure directions. It was concluded, moreover, that the vibration response characteristics of the hand and arm differ, depending upon whether the signal is a discrete frequency signal or a signal consisting of several frequencies.