  In this paper we analyze a virtual element method (VEM) for a pseudostress
formulation of the Stokes eigenvalue problem. This formulation allows to
eliminate the velocity and the pressure, leading to an elliptic formulation
where the only unknown is the pseudostress tensor. The velocity and pressure
can be recovered by a post-process. Adapting the non-compact operator theory,
we prove that our method provides a correct approximation of the spectrum and
is spurious free. We prove a priori error estimates, with optimal order, which
we confirm with some numerical tests.
