Nuclear criticality safety is a field of nuclear engineering dedicated to the prevention of nuclear and radiation accidents resulting from an inadvertent, self-sustaining nuclear chain reaction. Additionally, nuclear criticality safety is concerned with mitigating the consequences of a nuclear criticality accident. A nuclear criticality accident occurs from operations that involve fissile material and results in a tremendous and potentially lethal release of radiation. Nuclear criticality safety practitioners attempt to minimize the probability of a nuclear criticality accident by analyzing normal and abnormal fissile material operations and providing controls on the processing of fissile materials. A common practice is to apply a double contingency analysis to the operation in which two or more independent, concurrent and unlikely changes in process conditions must occur before a nuclear criticality accident can occur. For example, the first change in conditions may be complete or partial flooding and the second change a re-arrangement of the fissile material. Controls (requirements) on process parameters (e.g., fissile material mass, equipment) result from this analysis. These controls, either passive (physical), active (mechanical), or administrative (human), are implemented by inherently safe or fault-tolerant plant designs, or, if such designs are not practicable, by administrative controls such as operating procedures, job instructions and other means to minimize the potential for significant process changes that could lead to a nuclear criticality accident.

Seven factors influence a criticality system.

1. Geometry or shape of the fissile material: If neutrons escape (leak from) the fissile system they are not available to interact with the fissile material to cause a fission event. Therefore the shape of the fissile material affects the probability of occurrence of fission events. A large surface area such as a thin slab has lots of leakage and is safer than the same amount of fissile material in a small, compact shape such as a cube or a sphere.
2. Interaction of units: Neutrons leaking from one unit can enter another. Two units, which by themselves are sub-critical, could interact with each other to form a critical system. The distance separating the units and any material between them influences the effect.
3. Reflection: When neutrons collide with other atomic particles (primarily nuclei) and are not absorbed, they change direction. If the change in direction is large enough, the neutron may travel back into the system, increasing the likelihood of interaction (fission). This is called ‘reflection’. Good reflectors include hydrogen, beryllium, carbon, lead, uranium, water, polyethylene, concrete, Tungsten carbide and steel.
4. Moderation: Neutrons resulting from fission are typically fast (high energy). These fast neutrons do not cause fission as readily as slower (less energetic) ones. Neutrons are slowed down (moderated) by collision with atomic nuclei. The most effective moderating nuclei are hydrogen, deuterium, beryllium and carbon. Hence hydrogenous materials including oil, polyethylene, water, wood, paraffin, and the human body are good moderators. Note that moderation comes from collisions; therefore most moderators are also good reflectors.
5. Absorption: Absorption removes neutrons from the system. Large amounts of absorbers are used to control or reduce the probability of a criticality. Good absorbers are boron, cadmium, gadolinium, silver, and indium.
6. Enrichment: The probability of a neutron reacting with a fissile nucleus is influenced by the relative numbers of fissile and non-fissile nuclei in a system. The process of increasing the relative number of fissile nuclei in a system is called enrichment. Typically, low enrichment means less likelihood of a criticality and high enrichment means a greater likelihood.
7. Mass: The probability of fission increases as the total number of fissile nuclei increases. The relationship is not linear. There is a threshold below which criticality can not occur. This threshold is called the critical mass.

To determine whether a system containing fissile material is safe, calculations are performed using computer programmes. The analyst describes the geometry of the system and the materials, usually with conservative or pessimistic assumptions. The density and size of any neutron absorbers is minimised while the amount of fissile material is maximised. As some moderators are also absorbers, the analyst must be careful when modelling these to be pessimistic. Computer programmes allow analysts to describe a three dimensional system with boundary conditions. These boundary conditions can represent real boundaries such as concrete walls or the surface of a pond, or can be used to represent an artificial infinite system using a periodic boundary condition. These are useful when representing a large system consisting of many repeated units.

Computer codes used for criticality safety analyses include MONK(UK), KENO(USA), MCNP(USA) and CRISTAL(France).

Traditional criticality analyses assume that the fissile material is in its most reactive condition, which is usually at maximum enrichment, with no irradiation. For spent nuclear fuel storage and transport, burnup credit may be used to allow fuel to be more closely packed, reducing space and allowing more fuel to be handled safely. In order to implement burnup credit, fuel is modeled as irradiated using pessimistic conditions which produce an isotopic composition representative of all irradiated fuel. Fuel irradiation produces actinides consisting of both neutron absorbers and fissionable isotopes as well as fission products which absorb neutrons.

In fuel storage pools using burnup credit, separate regions are designed for storage of fresh and irradiating fuel. In order to store fuel in the irradiating fuel store it must satisfy a loading curve which is dependent on initial enrichment and irradiation.