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We have developed a new ultrasonic method for measuring the phase velocity of longitudinal and shear waves in self‐supporting thin films. The film is bonded at one end to an interdigital transducer (IDT) which emits a continuous wave signal. The film is supported at the other end and maintained flat under a weak tension. A receiving IDT detects the in‐phase and quadrature components of the sound waves as they propagate. A liquid bond is used between the receiving IDT and the film to allow a continuous variation of the path length. From the longitudinal and shear wave velocities, we can deduce the flexural and shear moduli of the film. For films of uniaxial or higher symmetry, the Young’s and biaxial moduli can be expressed as combinations of the flexural and shear moduli. We applied this technique to Cu‐Pd composition modulated thin films. Contrary to previous reports, we have not observed the supermodulus effect in either the flexural, shear, Young’s or biaxial moduli for modulation wavelengths between 13 and 36 Å.