The maximum amount of tensile stress that can be applied to a material over somewhere near 107 cycles without causing failure. The fatigue strength for a test with just one cycle is equal to the ultimate tensile strength (UTS). As the number of cycles increases, the value decreases.
Some metals (most steels, some brasses, and a few others) will eventually floor out, so that, past a certain number of cycles, the maximum allowed stress per cycle will no longer decrease. This is called the endurance limit, although the term may be used to refer to fatigue strength in general. Other materials will continue to see a decrease.
It is common to estimate fatigue strength as some fraction of UTS that is specific to a material type (e.g. 35% for austenitic stainless steels).
ASTM testing standards include C1361 for ceramics, D3479 for polymeric-matrix composites, D4482 for rubbers, D7774 for plastics, E466 for metals, and F1801 for corrosion fatigue of metals used in implants. ISO standards include 1099 for metals and 13003 for polymeric-matrix composites.
The above standards cover tensile (or axial) loading. Other standardized tests use flexural (bending) loading. They include ASTM B593, ISO 1143, ISO 22214, and ISO 28704. A few standards also exist for other loading types. If a fatigue strength value is determined under any loading other than tensile, that information needs to be communicated alongside the value.
For glass materials, the term static fatigue strength is used to refer to an unrelated property.