Vortex formation at intake is an important problem encountered in hydraulic engineering. When the submergence of the intake is not sufficient, air enters the intake by means of a free-surface vortex. The value of the intake's submergence when the vortex starts entraining air is known as "critical submergence". The main aim of this study is to develop a suitable model for the effect of circulation on the critical submergence of an intake. Therefore, an artificial neural network (ANN) and multi-linear regression (MLR) models are used. Vanes making angle with radial direction are used to give the circulation. Experiments were conducted on a vertically flowing downward intake pipe in a circulation imposed still-water reservoir. In this study, a suitable ANN model is developed by considering the feed-forward back propagation learning algorithm in the critical submergence for intake pipe. In the model angle of vane, velocity, distance from bottom to upper level of the intake pipe (clearance) is used for input variables and submergence ratio (ratio of critical submergence to intake pipe's diameter) is used for output. Results of these experimental studies are compared with those obtained by the ANN and MLR approaches. It was found that the obtained ANN model has a significant prediction power.