When a force $F$ acts along the surface area $A$ of a body—as opposed to elongation, where the force acts perpendicular to the surface—the side surfaces of the body are displaced by an angle $\gamma$. The applied forces are therefore referred to as shear forces.
Analogous to pressure, we define the shear stress as the force per area:
$$
\tau = \frac{F}{A}
$$
The body length increases by $\Delta \ell$ in the direction of the force.
Again, by analogy with Hooke’s law, the following relationship holds:
$$
\tau = G \frac{\Delta \ell}{\ell}
$$
The material constant $G$ is called the shear modulus or modulus of rigidity.
The shear angle $\gamma$ is related to the displacement as follows:
$$
\tan\gamma = \frac{\Delta \ell}{\ell}
$$
For small angles (typically $\gamma < 5^\circ$), the approximation $\tan\gamma \approx \gamma$ can be used.
Thus, for a given shear stress and shear modulus, the shear angle can be calculated as:
$$
\gamma = \frac{\tau}{G}
$$
The shear modulus, like compressibility, is a material-specific constant and can be found in technical literature.