  By using an equivalent form of the uniform Lopatinski condition for 1-shocks,
we prove that the stability condition found by the energy method in [A.
Morando, Y. Trakhinin, P. Trebeschi, Structural stability of shock waves in 2D
compressible elastodynamics, Math. Ann. 378 (2020) 1471-1504] for the
rectilinear shock waves in two-dimensional flows of compressible isentropic
inviscid elastic materials is not only sufficient but also necessary for
uniform stability (implying structural nonlinear stability of corresponding
curved shock waves). The key point of our spectral analysis is a delicate study
of the transition between uniform and weak stability. Moreover, we prove that
the rectilinear shock waves are never violently unstable, i.e., they are always
either uniformly or weakly stable.
