Abstract: It is assumed in this paper that for a high Reynolds number nearly homogeneous wind flow, the Reynolds stresses are uniquely related to the mean velocity gradients and the two independent turbulent scaling parameters k and ε. By applying dimensional analysis and owing to the Cayley-Hamilton theorem for tensors, a new turbulence enclosure model so called the extended k-ε model has been developed. The coefficients of the model expression were determined by the wind tunnel experimental data of homogeneous shear turbulent flow. The model was compared with the standard k-ε model in its composition and the prediction of the Reynolds normal stresses. Using the new model the numerical simulation of wind flow around a square cross-section tall building, was perfoumed. The results show that the extended k-ε model improves the prediction of wind velocities around the building and wind pressures on the building envelope.