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We report a Raman scattering investigation of InAs vibrational modes in multiple layers of InAs self-assembled quantum dots in a GaAs matrix. The Raman peak associated with quantum-dot phonons shows a downward frequency shift as the interlayer spacing decreases. We attribute this frequency shift to the relaxation of the elastic strain in the stacked quantum-dot layers. From the phonon frequency shift, we estimate the magnitude of the strain in the quantum dot layers, which we relate to the energy of the photoluminescence emission of the dots.