Laboratory experiments have been conducted to investigate the change in induced magnetization caused by triaxial stress variations on andesite specimens. Induced axial magnetization was found to decrease with the increment of axial load (as in the case for uniaxial stress conditions) for a constant confining pressure, while induced radial magnetization increased with axial load increments. This relationship between stress changes and induced magnetization variation was found to depend on the confining pressure magnitude and the maximum axial stress previously reached: the larger the confining pressure, the larger the effect on induced axial magnetization, but the smaller the effect on induced radial magnetization; the larger the maximum differential stress, the smaller the effect of stress variation on both axial and radial induced magnetization except for uniaxial stress condition. For small maximum differential stresses or maximum axial stress conditions close to the maximum load bearing capacity of the material, this relationship was found to be linear so that a tensorial formulation could be proposed for small magnetic fields. This led to the definition of a fourth-order tensor, which was called the piezomagnetic tensor. The important geophysical implications of these results is that the influence of deviatoric stress variations on induced magnetization increases with depth, provided the maximum differential stress supported in the past by the material is not close to that necessary for failure to occur; for this last instance the influence of a pure deviatoric stress variation is independent of the spherical component of the stress state. Accordingly, pore pressure variations could generate induced magnetization variations for those rocks which have not been loaded close to failure.