The strain rate at some point within the material measures the rate at which the distances of adjacent parcels of the material change with time in the neighborhood of that point.

The strain rate is a concept of materials science and continuum mechanics that plays an essential role in the physics of fluids and deformable solids.

In an isotropic Newtonian fluid, in particular, the viscous stress is a linear function of the rate of strain, defined by two coefficients, one relating to the expansion rate (the bulk viscosity coefficient) and one relating to the shear rate (the "ordinary" viscosity coefficient).

In solids, higher strain rates can often cause normally ductile materials to fail in a brittle manner.

The strain is the ratio of two lengths, so it is a dimensionless quantity (a number that does not depend on the choice of measurement units).

For example, when a long and uniform rubber band is gradually stretched by pulling at the ends, the strain can be defined as the ratio

The strain rate can also be expressed by a single number when the material is being subjected to parallel shear without change of volume; namely, when the deformation can be described as a set of infinitesimally thin parallel layers sliding against each other as if they were rigid sheets, in the same direction, without changing their spacing.

Then the strain in each layer can be expressed as the limit of the ratio between the current relative displacement

In more general situations, when the material is being deformed in various directions at different rates, the strain (and therefore the strain rate) around a point within a material cannot be expressed by a single number, or even by a single vector.

In such cases, the rate of deformation must be expressed by a tensor, a linear map between vectors, that expresses how the relative velocity of the medium changes when one moves by a small distance away from the point in a given direction.

This strain rate tensor can be defined as the time derivative of the strain tensor, or as the symmetric part of the gradient (derivative with respect to position) of the velocity of the material.

With a chosen coordinate system, the strain rate tensor can be represented by a symmetric 3×3 matrix of real numbers.

It only describes the local rate of deformation to first order; but that is generally sufficient for most purposes, even when the viscosity of the material is highly non-linear.

Engineering sliding strain can be defined as the angular displacement created by an applied shear stress,