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Mechanical Q-factor measurements of single crystalline calcium fluoride CaF2bulk material are presented. Resonant modes between 27 and 100?kHz were investigated on a cylindrical test sample ([Formula: see text][Formula: see text]75?mm ?75?mm). For selected modes low temperature measurements of the mechanical Q-factor were done within a temperature range from 5 to 300?K. For the Q-measurements a ring-down technique was used. The substrate was suspended as a pendulum by means of a tungsten wire loop. The highest Q-factor has been achieved around 60?K with 3 ?108which is the highest Q-factor reported on CaF2up to now. [ABSTRACT FROM AUTHOR]