The adiabatic elastic moduli of hexagonal close‐packed lutetium single crystals have been determined by the ultrasonic pulse superposition technique over the temperature range 4.2–300°K. The values at 300°K in units of 1011dyn/cm2areC11=8.62,C33=8.09,C44=2.68,C66=2.71, andC13=2.8; the values extrapolated to 0°K areC11=9.10,C33=8.40,C44=2.91,C66=2.96, andC13=2.9. The Debye temperature calculated using the elastic moduli at 0°K is 184.5°K. The bulk elastic properties have also been calculated and they agree favorably with previously predicted polycrystalline values. The linear thermal‐expansion coefficients of the lutetium single crystals have been determined over the same temperature range by using a linear‐variable‐differential‐transformer dilatometer. The room‐temperature coefficients of thermal expansion are &agr;∥=2.0×10−6and &agr;⊥=4.82×10−6°K−1. A maximum in &agr;⊥was found at 130°K, which apparently correlates with the maximum found in the &ggr;⊥/&ggr;∥ratio at 130°K, where &ggr; is the Gru¨neisen constant.