Single crystals of MoSi2 and WSi2 with a body-centred-tetragonal C 1 1b structure were fabricated using a floating-zone method. The elastic wave velocity was measured for samples with various orientations using a simple pulse echo method at room temperature, and six elastic stiffness constants cij were calculated. The stiffness constants were a little higher for WSi2 than for MoSi2. c11 and c33 of these compounds were approximately equal to c11 of tungsten and molybdenum, respectively, although cij (i ≠j) was a little higher for these compounds than for molybdenum and tungsten. Young's modulus 1/s11 was the highest in the <0 0 1> direction, and the lowest in the <1 0 0> direction. The shear modulus 1/s66 was high on the {0 0 1} plane and independent of shear direction. It was generally low on the close-packed {1 1 0} plane and largely dependent on shear direction. The elastic constants for the polycrystalline materials were estimated from cij and sij. Poisson's ratio v was 0.15 for MoSi2 and for WSi2, and these values were much lower than for ordinary metals and alloys. The Debye temperature θD was estimated using the elastic-wave velocity of the polycrystalline materials via the elastic constants such as Young's modulus and shear modulus: it was 759 K for MoSi2 and 625 K for WSi2. © 1990 Chapman and Hall Ltd.