This paper presents instability analyses, such as elasto-plastic finite displacement analysis under in-plane load, finite displacement analysis under displacement-dependent wind load and flutter analysis based on modal coordinate, which identify static and dynamic instabilities of long-span cable-stayed bridges. Using 1400-meter cable-stayed bridge models with four types of cross sectional shapes of the girder, whose span-to-width and span-to-depth ratios are considerably large compared with those used in past long-span conventional cable-stayed bridges, instability analyses are carried out. From these calculations, a minimum cross sectional shape ensuring safety against static and dynamic instabilities was presented. It was found that instability under static wind load is the most critical, but that the span-to-girder width ratio can be greater than the widely-believed value of 40.