External loads are carried through a solid by internal forces distributed across imagined cut surfaces. Stress measures this internal force per unit area.

Normal stress

If an axial force $F$ acts uniformly over cross-sectional area $A$, the average normal stress is

$$\sigma=\frac{F}{A}.$$

Tensile normal stress pulls material apart; compressive normal stress pushes it together.

Shear stress

When the internal force acts parallel to a surface, the average shear stress is

$$\tau=\frac{F}{A}.$$

The same units are used for normal and shear stress: pascals in SI.

Stress is local

The simple formulas above give average stress. In real components the stress can vary strongly across a section, especially near holes, notches, contacts and changes in geometry.

Stress provides the bridge from whole-body force equilibrium to the local mechanical state of a material.