  We study generalised Navier--Stokes equations governing the motion of an
electro-rheological fluid subject to stochastic perturbation. Stochastic
effects are implemented through (i) random initial data, (ii) a forcing term in
the momentum equation represented by a multiplicative white noise and (iii) a
random character of the variable exponent $p=p(\omega,t,x)$ (as a result of a
random electric field). We show the existence of a weak martingale solution
provided the variable exponent satisfies $p\geq p^->\frac{3n}{n+2}$ ($p^->1$ in
two dimensions). Under additional assumptions we obtain also pathwise
solutions.
