  A notion of Poincar\'e series was introduced by A.Campillo et al. It was
developed by Delgado and Gusein-Zade for a multi-index filtration corresponding
to the sequence of blow-ups. The present paper suggests the way to generalize
the notion of Poincar\'e series to the case of arbitrary locally free sheaf on
the modification of complex plane $\mathbb{C}^2$.
  This series is expressed through the topological invariants of the sheaf. For
the sheaf of holomorphic functions the answer coincides with the Poincar\'e
series found before.
