  In this paper, we establish the well-posedness for the third grade fluid
equation perturbed by a multiplicative white noise. This equation describes the
motion of a non-Newtonian fluid of differential type with relevant viscoelastic
properties. We are faced with a strongly nonlinear stochastic partial
differential equation supplemented with a Navier slip boundary condition.
Taking the initial condition in the Sobolev space H^2, we show the existence
and the uniqueness of the strong (in the probability sense) solution in a two
dimensional and non axisymmetric bounded domain.
