  We consider the approximation of eigenvalue problems for elasticity equations
with interface. This kind of problems can be efficiently discretized by using
immersed finite element method (IFEM) based on Crouzeix-Raviart
P1-nonconforming element. The stability and the optimal convergence of IFEM for
solving eigenvalue problems with interface are proved by adapting spectral
analysis methods for the classical eigenvalue problem. Numerical experiments
demonstrate our theoretical results.
