  In this paper we analyze a mixed displacement-pseudostress formulation for
the elasticity eigenvalue problem. We propose a finite element method to
approximate the pseudostress tensor with Raviart-Thomas elements and the
displacement with piecewise polynomials. With the aid of the classic theory for
compact operators, we prove that our method is convergent and does not
introduce spurious modes. Also, we obtain error estimates for the proposed
method. Finally, we report some numerical tests supporting the theoretical
results.
