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We present here a theoretical study of eigenmodes inaxisymmetric elastic layers.The mathematical modelling allows us to bring this problem to a spectral studyof a sequence of unbounded self-adjoint operators A n , $n\in \mathbb{N}$ 
, in a suitableHilbert space. We show that the essential spectrum of A n is an interval oftype $[\gamma,+\infty[$ 
and that, under certain conditions on the coefficientsof the medium, the discrete spectrum is non empty.
