  We consider the approximation of elliptic eigenvalue problem with an immersed
interface. The main aim of this paper is to prove the stability and convergence
of an immersed finite element method (IFEM) for eigenvalues using
Crouzeix-Raviart $P_1$-nonconforming approximation. We show that spectral
analysis for the classical eigenvalue problem can be easily applied to our
model problem. We analyze the IFEM for elliptic eigenvalue problem with an
immersed interface and derive the optimal convergence of eigenvalues. Numerical
experiments demonstrate our theoretical results.
