Crystalline silicon has been proposed as a new test mass material in third generation gravitational wave detectors such as the Einstein telescope (ET). Birefringence can reduce the interferometric contrast and can produce dynamical disturbances in interferometers. In this work we use the method of polarization-dependent resonance-frequency analysis of Fabry-Perot-cavities containing silicon as a birefringent medium. Our measurements show a birefringence of silicon along the (111) axis of the order of Δ n ≈ 10-7 at a laser wavelength of 1550 nm and room temperature. A model is presented that explains the results of different settings of our measurements as a superposition of elastic strains caused by external stresses in the sample and plastic strains possibly generated during the production process. An application of our theory on the proposed ET test mass geometry suggests no critical effect on birefringence due to elastic strains.