A stress field is the distribution of internal forces in a body that balances a given set of external forces. Stress fields are widely used in fluid dynamics and materials science. Consider that one can imagine stress fields as the stress created by adding an additional half-plane of atoms to a crystal. The bonds clearly stretch around the location of the dislocation "Dislocation (crystal defect)") and this stretching causes the stress field to form. Atomic bonds further and further from the dislocation center are less and less stretched, so the stress field dissipates as the distance from the dislocation center increases. Each dislocation within the material has an associated stress field. The creation of these stress fields is a result of the material attempting to dissipate the mechanical energy being exerted on the material. By convention, these dislocations are labeled positive or negative, depending on whether the dislocation stress field is primarily compressive or tensile.

By modeling dislocations and their stress fields as positive (compression field) or negative charges ("Stress (mechanical)" field) we can understand how dislocations interact with each other in the network. If two similar fields come into contact with each other, they will be rejected by each other. On the other hand, if two opposite charges come into contact with each other, they will be attracted to each other. These two interactions will strengthen the material in different ways. If two fields with equivalent charge come into contact and are limited to a particular region, an excessive force is needed to overcome the repulsive forces necessary to cause dislocation motion relative to each other. If two oppositely charged fields come into contact with each other, they will merge with each other to form a thrust. A thrust can be modeled as a potential well that traps dislocations. Therefore, excessive force is needed to separate the dislocations. Since dislocation motion is the primary mechanism behind plastic deformation, increasing the stress required to move dislocations directly increases the yield strength of the material.

Stress field theory can be applied to various strengthening mechanisms for materials. Stress fields can be created by adding atoms of different sizes to the lattice (solute strengthening). If a smaller atom is added to the lattice, a tensile stress field is created. Atomic bonds are longer due to the smaller radius of the solute atom. Likewise, if a larger atom is added to the lattice, a compressive stress field is created. Atomic bonds are shorter due to the larger radius of the solute atom. The stress fields created by adding solute atoms form the basis of the material strengthening process that occurs in alloys.