right|thumb|300px|The second-order Cauchy stress tensor describes the stress experienced by a material at a given point. For any unit vector , the product is a vector, denoted , that quantifies the force per area along the plane perpendicular to . This image shows, for cube faces perpendicular to , the corresponding stress vectors along those faces. Because the stress tensor takes one vector as input and gives one vector as output, it is a second-order tensor.
right|thumb|300px|The second-order Cauchy stress tensor describes the stress experienced by a material at a given point. For any unit vector , the product is a vector, denoted  that quantifies the force per area along the plane perpendicular to . This image shows, for cube faces perpendicular to , the corresponding stress vectors along those faces. Because the stress tensor takes one vector as input and gives one vector as output, it is a second-order tensor.