Side weirs are diversion structures extensively used in irrigation, flood protection and combined sewer systems. Accurate estimation of the discharge coefficient (Cd) of side weirs is essential to compute the water surface profile over the weirs and to determine the lateral outflow rate from the system. In this paper, we have utilized a linear genetic programming (LGP) technique to develop new empirical formulas for the estimation of Cd of sharp-edged rectangular side weirs located in circular channels. For this aim, we have employed a total of 1,686 laboratory experimental observations in both sub- and supercritical flow regimes in order to train and validate the proposed models. The performance of the LGP-based models was also compared with those of different multilinear and nonlinear regression models in terms of root mean squared errors, mean absolute errors, and determination coefficient. The results indicated that an explicit LGP-based model using only mathematical functions could be employed successfully in Cd estimation in both sub- and supercritical flow conditions. Genetic-based sensitivity analysis among the input parameters demonstrated that Froude number at upstream of the weir has the most impact on the Cd estimation.