Solid rubber tires cannot go flat. They can get damaged, but it is unlikely that one incident will render a solid rubber tire inoperable, as can happen to a pneumatic tire. Pneumatic tires offer better shock absorption for a smoother ride and are much lighter than solid rubber tires.
Pneumatic tires are used almost exclusively where weight and ride comfort are a factor, such as on automobiles and aircraft. Solid rubber tires are popular in terrain that could pose puncture hazards to rubber tires, and where ride comfort and weight are less of a factor. Tractors, forklifts and similar equipment often use solid rubber tires.