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Our aim in this paper is to determine the tautological algebra generated bythe cohomology classes of the Brill Noether loci in the rational cohomology ofthe moduli stack $\mathcal{U}_C(n,d)$ of semistable bundles of rank $n$ anddegree $d$. When $C$ is a general smooth projective curve of genus $g\geq 2$,$n=2$, $d=2g-2$, the tautological algebra of $ \mathcal{U}_C(2,2g-2)$ (resp.$\mathcal{SU}_C(2,L)$, $deg(L)=2g-2)$) is generated by the divisor classes(resp. the Theta divisor $\Theta$).

Tautological algebra of the moduli stack of semi stable bundles of rank two on a general curve