Sandwich theory describes the behaviour of a beam, plate, or shell which consists of three layers—two facesheets and one core. The most commonly used sandwich theory is linear and is an extension of first-order beam theory. The linear sandwich theory is of importance for the design and analysis of sandwich panels, which are of use in building construction, vehicle construction, airplane construction and refrigeration engineering.

Some advantages of sandwich construction are:

The behavior of a beam with sandwich cross-section under a load differs from a beam with a constant elastic cross section. If the radius of curvature during bending is large compared to the thickness of the sandwich beam and the strains in the component materials are small, the deformation of a sandwich composite beam can be separated into two parts

Sandwich beam, plate, and shell theories usually assume that the reference stress state is one of zero stress. However, during curing, differences of temperature between the facesheets persist because of the thermal separation by the core material. These temperature differences, coupled with different linear expansions of the facesheets, can lead to a bending of the sandwich beam in the direction of the warmer facesheet. If the bending is constrained during the manufacturing process, residual stresses can develop in the components of a sandwich composite. The superposition of a reference stress state on the solutions provided by sandwich theory is possible when the problem is linear. However, when large elastic deformations and rotations are expected, the initial stress state has to be incorporated directly into the sandwich theory.

In the engineering theory of sandwich beams, the axial strain is assumed to vary linearly over the cross-section of the beam as in Euler-Bernoulli theory, i.e.,

Therefore, the axial stress in the sandwich beam is given by

where ${\displaystyle E(z)}$ is the Young's modulus which is a function of the location along the thickness of the beam. The bending moment in the beam is then given by

The quantity ${\displaystyle D}$ is called the flexural stiffness of the sandwich beam. The shear force ${\displaystyle Q_{x}}$ is defined as