Understanding morphological changes of a river system is a necessary part of river management plans. Accurate assessment of the stability of alluvial channels is a significant issue in the design and retrofit of urban streams adversely impacted by rapid urbanization and climate change. In the present study, an evolutionary polynomial regression (EPR) model was designed to estimate the width (W), depth (D), and slope (S) of a stable channel based on a wide range of field and experimental datasets in sand, gravel and mountain rivers. Furthermore, the effect of 4 influential input parameters of mean sediment size (d50), flow discharge (Q), the Shields parameter (τ) and free water surface slope (S) of channel on the dimensions of stable alluvial channels is investigated using EPR model and a novel designed Gene Expression Programming (GEP) model. In addition, in the present study, the performance of 15 previous popular traditional methods in estimating stable channel dimensions is reviewed and compared with the results of the proposed models. The results show that the EPR model (Root Mean Square Error (RMSE)=0.4, Bias = -0.04 and determination coefficient (R2)=0.925) has less error than GEP model (RMSE = 0.45, Bias = -0.08, R2 = 0.918) and by providing a simpler polynomial relationship than the GEP model, it is more accurate. The EPR and GEP models in addition to suggesting robust and straightforward relationships have higher accuracy than traditional models, especially in predicting the width and depth of the flow. The parametric analysis shows that Shields parameter (τ) is an effective parameter in predicting the channel slope. The developed GEP and EPR models with similar physical behavior to the best traditional methods have nonlinear variations respect to τ. The EPR relationships presented in this study can be used as an alternative to traditional relationships with higher accuracy and easier usability in the design and implementation of stable channels.