A mathematical model of the formation of submarine gullies due to turbidity currents is presented in this study. A linear stability analysis is performed with the use of layer-averaged momentum equations of turbidity currents, a dispersion equation of suspended sediment, and the Exner equation extended for the seabed subject to erosion and deposition due to turbidity currents. The analysis shows that the dominant gully spacing is of the order of 1500--8000 times the Richardson-critical layer thickness of turbidity currents. Evaluating the Richardson-critical layer thickness to be of the order of 0.1--1.0 m, the spacing of submarine gullies is of the order of 150--8000 m. According to observations, the spacing of submarine gullies ranges from a few hundred meters to a few kilometers. The theoretical results are found to be consistent with the observations.