A matrix method for tensor transformations in Voigt notation known from the elasticity calculations has been applied to elasto-optical calculations. Using invariant tensor-to-matrix mapping, the second- and fourth-rank Cartesian tensor transformations and basic operations can be performed by means of matrix multiplication. This approach brings what we believe is a new method of correct tensorial operations in Voigt notation, replacing a well-known approach that allocated specific constants to some matrix elements to even up the difference between the tensor transformations and 6 × 6 matrix operations. This general approach also simplifies the use of elasto-optical calculations for an arbitrary crystal class in an arbitrary orientation.