A non-Newtonian fluid is a fluid whose flow properties differ in any way from those of Newtonian fluids. Most commonly the viscosity (measure of a fluid's ability to resist gradual deformation by shear or tensile stresses) of non-Newtonian fluids is dependent on shear rate or shear rate history. However, there are some non-Newtonian fluids with shear-independent viscosity, that nonetheless exhibit normal stress-differences or other non-Newtonian behavior. Many salt solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as ketchup, custard, toothpaste, starch suspensions, paint, blood, and shampoo. In a Newtonian fluid, the relation between the shear stress and the shear rate is linear, passing through the origin, the constant of proportionality being the coefficient of viscosity. In a non-Newtonian fluid, the relation between the shear stress and the shear rate is different, and can even be time-dependent. Therefore, a constant coefficient of viscosity cannot be defined.

Although the concept of viscosity is commonly used in fluid mechanics to characterize the shear properties of a fluid, it can be inadequate to describe non-Newtonian fluids. They are best studied through several other rheological properties which relate stress and strain rate tensors under many different flow conditions, such as oscillatory shear, or extensional flow which are measured using different devices or rheometers. The properties are better studied using tensor-valued constitutive equations, which are common in the field of continuum mechanics.
Shear thinning fluid: A familiar example of the opposite, a shear thinning fluid, or pseudoplastic fluid, is wall paint: one wants the paint to flow readily off the brush when it is being applied to the surface being painted, but not to drip excessively. Note that all thixotropic fluids are extremely shear thinning, but they are significantly time dependent, whereas the colloquial "shear thinning" fluids respond instantaneously to changes in shear rate. Thus, in order to avoid confusion, the latter classification is more clearly termed pseudoplastic.
Bingham plastic: There are fluids which have a linear shear stress/shear strain relationship which require a finite yield stress before they begin to flow (the plot of shear stress against shear strain does not pass through the origin). These fluids are called Bingham plastics. Several examples are clay suspensions, drilling mud, toothpaste, mayonnaise, chocolate, and mustard. The surface of a Bingham plastic can hold peaks when it is still. By contrast Newtonian fluids have flat featureless surfaces when still.
Rheopectic: There are also fluids whose strain rate is a function of time. Fluids that require a gradually increasing shear stress to maintain a constant strain rate are referred to as rheopectic. An opposite case of this, is a fluid that thins out with time and requires a decreasing stress to maintain a constant strain rate (thixotropic).
Many common substances exhibit non-Newtonian flows. These include:

• Soap solutions and cosmetics
• Food such as butter, cheese, jam, ketchup, mayonnaise, soup, and yogurt
• Natural substances such as magma, lava, gums, and extracts such as vanilla extract. Ketchup is a shear thinning fluid. Shear thinning means that the fluid viscosity decreases with increasing shear stress. In other words, fluid motion is initially difficult at slow rates of deformation, but will flow more freely at high rates.
• Biological fluids such as blood, saliva, semen, and synovial fluid
• Slurries such as cement slurry, emulsions such as mayonnaise, and some kinds of dispersions