Three-dimensional modelling of the floating zone (needle-eye) crystal growth process is carried out to analyse numerically the stability of the melt flow and the influence of the crystal rotation rate and inductor slit width on the 3D flow field and on the grown crystal resistivity. The unsteadiness of the melt is simulated and it is found that for the considered growth parameters a steady-state flow can be a reasonable approximation to the unsteady melt motion. The parametric studies have shown that increasing the rotation rate essentially changes the flow pattern and weakens the rotational striations, while the inductor slit width has a more local influence on these characteristics.