When a viscous liquid bridge between two parallel substrates is stretched by accelerating one substrate, its interface on the plates recedes in the radial direction. In some cases the interface becomes unstable. Such instability leads to the emergence of a network of fingers. In this study, the mechanisms of such fingering are studied experimentally and analysed theoretically. The experimental set-up allows a constant acceleration of a movable substrate at up to 180 m s$^{-2}$. The phenomena are observed using two high-speed video systems. The number of fingers is measured for different liquid viscosities, liquid bridge sizes and wetting conditions. Linear stability analysis of the bridge interface takes into account the inertial, viscous and capillary effects in the liquid flow. The theoretically predicted maximum number of fingers, corresponding to an instability mode with the maximum amplitude, and a threshold for the onset of finger formation are proposed. Both models agree well with the experimental data up to the start of emerging cavitation bubbles.