Summary: A stochastic version of modified Navier-Stokes equations introduced by G. Prouse [Nonlinear Anal. 289–305 (1991)] is considered in a three-dimensional torus; its main feature is that instead of the linear term \(-\nu \Delta u\) of Navier-Stokes equations there is a nonlinear term \(-\Delta \Phi (u) - \nabla \operatorname{div} \Phi (u)\). First, for this equation we prove existence and uniqueness of martingale solutions; then existence of stationary solutions. In the last part of the paper a new model, obtained from Prouse model with the nonlinearity \(\Phi (u)=\nu |u|^{4}u\), is analysed; for the structure function of this model, we present some insights towards an expression similar to that obtained by the Kolmogorov 1941 theory of turbulence.