  The aim of this paper is to give a precise proof of the completeness of Lamb
modes and associated modes. This proof is relatively simple and short but
relies on two powerful mathematical theorems. The first one is a theorem on
elliptic systems with a parameter due to Agranovich and Vishik. The second one
is a theorem due to Locker which gives a criterion to show the completeness of
the set of generalized eigenvectors of a Hilbert-Schmidt discrete operator.
