A mathematical model of the formation of submarine canyons due to turbidity currents is presented in this study. A linear stability analysis is performed with the use of the momentum equations of turbidity currents, the dispersion equation of suspended sediment, and the Exner equation extended for sea beds subject to erosion due to turbidity currents. The analysis shows that the dominant channel spacing is of the order of 1500-8000 times the Richardson-critical layer thickness of turbidity currents. Evaluating the Richardson-critical thickness is of the order of 0.1-1.0m, the spacing of young canyons is of the order of 150-8000m. The theoretical results are found to agree resonably well with the observation.