Due to its importance in flow measurement and instrumentation, as well as its frequent application in differential pressure flowmeters, orifice discharge coefficient (Cd) needs to be estimated precisely. In this study, different soft computing models (including multiple linear regression (MLR), group method of data handling (GMDH), multivariate adaptive regression splines (MARS), M5P tree model, and random forest (RF)) were employed for the first time in estimation of the Cd value, and their respective prediction performances were analyzed statistically. Coefficient of correlation (CC), mean absolute error (MAE), root mean square error (RMSE), scattering index (SI), and Nash–Sutcliffe model efficiency coefficient (NSE) were used as the statistical indicators for validating the performance of each soft computing model. The statistical indicators approved the superiority of the RF model over the other models, while the MARS model also showed a competitive prediction potential over M5P, GMDH, and MLR models. The findings of this computational study clearly demonstrated that the implemented soft computing strategy had the capability to be used in precise estimation of the Cd of the orifice meter, specifically, in situations where the measurement of the parameters in deterministic equation is not practically feasible.