forces are distributed continuously within the volume of the object. In engineering, e.g., structural, mechanical, or geotechnical, the stress distribution within an object, for instance stresses in a rock mass around a tunnel, airplane wings, or building columns, is determined through a stress analysis. Calculating the stress distribution implies the determination of stresses at every point (material particle) in the object. According to Cauchy, the stress at any point in an object (Figure 2), assumed as a continuum, is completely defined by the nine stress components of a second order tensor of type (2,0) known as the Cauchy stress tensor, : After the stress distribution within the object has been determined with respect to a coordinate system , it may be necessary to calculate the components of the stress tensor at a particular material point with respect to a rotated coordinate system , i.e., the stresses acting on a plane with a different orientation passing through that point of interest —forming an angle with the coordinate system (Figure 3). For example, it is of interest to find the maximum normal stress and maximum shear stress, as well as the orientation of the planes where they act upon. To achieve this, it is necessary to perform a tensor transformation under a rotation of the coordinate system. From the definition of tensor, the Cauchy stress tensor obeys the tensor transformation law. A graphical representation of this transformation law for the Cauchy stress tensor is the Mohr circle for stress. Mohr's circle for two-dimensional state of stress In two dimensions, the stress tensor at a given material point with respect to any two perpendicular directions is completely defined by only three stress components. For the particular coordinate system these stress components are: the normal stresses and , and the shear stress . From the balance of angular momentum, the symmetry of the Cauchy stress tensor can be demonstrated. This symmetry implies that . Thus, the Cauchy stress tensor can be written as: The objective is to use the Mohr circle to find the stress components and on a rotated coordinate system , i.e., on a differently oriented plane passing through and perpendicular to the - plane (Figure 4). The rotated coordinate system makes an angle with the original coordinate system . Equation of the Mohr circle To derive the equation of the Mohr circle for the two-dimensional cases of plane stress and plane