This paper reports the newly developed three-dimensional analytical wake models for single and multiple wind turbines. Firstly, the average wind speed of a single wind turbine is studied based on the single wake model. For a single wind turbine, assuming the incoming wind is distributed as power law in the vertical direction, the average wind speeds have a close relationship to the power exponent alpha, the hub height h(0) and the rotor radius r(0). When alpha = 0.4, the average wind speed can decrease to 96% of the speed at the hub height. Secondly, the three-dimensional multiple wake model is developed based on the single wake model. The method of Sum of Squares is applied to solve the wake adding problem. The available wind tunnel experimental data of two different layouts are used to validate the wake model. At the three representative heights, the wake model predicts the distribution of wind speed accurately. For Layout 1, at the hub and the top heights, most of the relative errors between the wake model results and the experimental data are smaller than 6%. At the top height, all relative errors are smaller than 20%. For Layout 2, the largest errors of the wake model are 8.5% at the top height, 17.8% at the bottom height and 21.2% at the hub height. The results predicted by the multiple wake model are demonstrated as well. The presented wake model can be used to describe the wind distribution and optimize the layout of wind farm. (C) 2019 Elsevier Ltd. All rights reserved.