  In this article we study Brill-Noether loci of moduli space of stable bundles
over smooth surfaces. We define Petri map as an analogy with the case of
curves. We show the non-emptiness of certain Brill-Noether loci over very
general quintic hypersurface in $\mathbb{P}^3$, and use the Petri map to
produce components of expected dimension.
