  In this paper, we consider the stochastic %equations of incompressible
non-Newtonian fluids driven by a cylindrical Wiener process $W$ with shear rate
dependent on viscosity in a bounded Lipschitz domain $D\in \mathbb{R}^n$ during
the time interval $(0,T)$. For $q>\frac{2n+2}{n+2}$ in the growth conditions
(1.2), we prove the existence of a martingale weak solution with $\nabla\cdot
u=0$ by using a pressure decomposition which is adapted to the stochastic
setting, the stochastic compactness method and the $L^\infty$-truncation.
