S U M M A R YThe basic existence-uniqueness theory for Stoneley waves propagating along a plane interface between different isotropic elastic media is re-examined, using a matrix formulation of the secular equation. The resulting development is appreciably simpler than previous treatments of the theory. The domain of existence of Stoneley waves and the limiting curves forming its outer boundary are characterized in terms of coordinates p:/p: and p2/pI where p , , p 2 are the shear moduli and / j I , p2 the speeds of transverse plane waves in the constituent media. The equations of the limiting curves are given explicitly and exemplified numerically.

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