In this paper, for the first time, the impact of the shape factor on the discharge coefficient of side orifices is evaluated using the novel Extreme Learning Machine (ELM) model. In addition, the Monte Carlo simulations (MCs) are applied to assess the accuracy of the modelling. Furthermore, the validation is conducted by means of the k-fold cross-validation approach (with k = 5). In other words, the most optimized number of hidden neurons is chosen to be equal to 30 and the results of all activation functions of the extreme learning machine are examined and the sigmoid activation function is selected for simulating the discharge coefficient. Subsequently, two modelling combinati0ons are introduced using the input parameters and five different extreme learning machine models are also developed. The analysis of the modelling results exhibits that the model with the shape factor is more accurate. The superior model is a function of all input parameters reasonably estimating the discharge coefficient. For example, the values of R and MAPE for this model are estimated to be 0.990 and 0.223, respectively. The results of the superior model are also compared with the empirical equations and it was shown that this model has higher accuracy.