Thermal noise in test mass substrates and coatings is a significant noise contribution in the detection band of current and proposed future gravitational wave detectors. Substrate thermal noise can be reduced by using high mechanical Q-factor materials and cooling the test mass mirrors. Silicon is a promising potential candidate for the next generation detector test masses. The low thermal expansion and high thermal conductivity of silicon allow efficient cryogenic operation, and a significant increase in the amount of optical power that can be used in the detectors by decreasing thermal deformation and aberration. Mechanical stress, damage, poor surface quality or contamination can result in increased loss and thermal noise. Therefore, the characterization of mechanical loss in silicon test masses is necessary. In this project, we developed a technique to measure high Q-factor mechanical modes. We used finite element modeling to optimize the design of the test mass support structure to minimize the loss coupling from the support structure over a wide frequency range. Mechanical Q-factors of the order of 107 were achieved for several modes of a 10 cm diam. × 3 cm cylindrical silicon test mass with such a support at room temperature.