SUMMARY This study intends to improve the predictability of the existing second-order closure turbulence models without tuning the model constants. For this purpose, a Reynolds stress model with a cross diffusion of κ in the ϵ equation is derived based on the physically more realistic assumption that small turbulent eddies can be anisotropic. The proposed Reynolds stress model differs from the existing Reynolds stress model in two aspects; an anisotropic dissipation model, , is adopted, and an additional cross diffusion term, Cϵ 3 ϵ/ κ ∂(κ 2/ ϵ ∂κ/∂ Xt)/∂ Xt is included in the ϵ equation. The proposed Reynolds stress turbulence model (RSMX), the existing Reynolds stress model (RSM) and a two-equation eddy viscosity model, the κ - ϵ model, are then tested in three turbulent free shear flows, namely plane jet, round jet, and plane mixing layer flows. It is shown that the proposed RSMX of turbulence model performs better than the existing turbulence models in all the three free shear flows concerned.