In materials science, photoelasticity describes changes in the optical properties of a material under mechanical deformation. It is a property of all dielectric media and is often used to experimentally determine the stress distribution in a material.

The photoelastic phenomenon was first discovered by the Scottish physicist David Brewster, who immediately recognized it as stress-induced birefringence. That diagnosis was confirmed in a direct refraction experiment by Augustin-Jean Fresnel. Experimental frameworks were developed at the beginning of the twentieth century with the works of E.G. Coker and L.N.G. Filon of University of London. Their book Treatise on Photoelasticity, published in 1930 by Cambridge Press, became a standard text on the subject. Between 1930 and 1940, many other books appeared on the subject, including books in Russian, German and French. Max M. Frocht published the classic two volume work, Photoelasticity, in the field. At the same time, much development occurred in the field – great improvements were achieved in technique, and the equipment was simplified. With refinements in the technology, photoelastic experiments were extended to determining three-dimensional states of stress. In parallel to developments in experimental technique, the first phenomenological description of photoelasticity was given in 1890 by Friedrich Pockels, however this was proved inadequate almost a century later by Nelson & Lax as the description by Pockels only considered the effect of mechanical strain on the optical properties of the material.

With the advent of the digital polariscope – made possible by light-emitting diodes – continuous monitoring of structures under load became possible. This led to the development of dynamic photoelasticity, which has contributed greatly to the study of complex phenomena such as fracture of materials.

Photoelasticity has been used for a variety of stress analyses and even for routine use in design, particularly before the advent of numerical methods, such as finite elements or boundary elements. Digitization of polariscopy enables fast image acquisition and data processing, which allows its industrial applications to control quality of manufacturing process for materials such as glass and polymer. Dentistry utilizes photoelasticity to analyze strain in denture materials.

Photoelasticity can successfully be used to investigate the highly localized stress state within masonry or in proximity of a rigid line inclusion (stiffener) embedded in an elastic medium. In the former case, the problem is nonlinear due to the contacts between bricks, while in the latter case the elastic solution is singular, so that numerical methods may fail to provide correct results. These can be obtained through photoelastic techniques. Dynamic photoelasticity integrated with high-speed photography is utilized to investigate fracture behavior in materials. Another important application of the photoelasticity experiments is to study the stress field around bi-material notches. Bi-material notches exist in many engineering application like welded or adhesively bonded structures.^{[citation needed]}

For example, some elements of Gothic cathedrals previously thought decorative were first proved essential for structural support by photoelastic methods.

For a linear dielectric material the change in the inverse permittivity tensor ${\displaystyle \Delta (\varepsilon ^{-1})_{ij}}$ with respect to the deformation (the gradient of the displacement ${\displaystyle \partial _{\ell }u_{k}}$) is described by

where ${\displaystyle P_{ijk\ell }}$ is the fourth-rank photoelasticity tensor, ${\displaystyle u_{\ell }}$ is the linear displacement from equilibrium, and ${\displaystyle \partial _{l}}$ denotes differentiation with respect to the Cartesian coordinate ${\displaystyle x_{l}}$. For isotropic materials, this definition simplifies to