Baffled chutes are used in irrigation systems, storm water systems, wastewater canal chutes, river training, and drop structures for energy dissipation. Two flow regions occur on the flow surface of baffled chutes. These are black water and white water regions. Knowing the location of the inception point where white water begins to appear on the surface is important for determination of the non-aerated flow region. Thus, cavitation damage can be prevented. In this study, 160 laboratory test results have been used for determining black water length (i.e., length of the non-aerated region) of baffled chutes with stepped, wedge, trapezoidal, and T-shaped baffle blocks. The obtained observation data have been analyzed by well-known soft computing methods such as artificial neural networks (ANN), curve fitting (CF), non-linear regression (NLR) and special extreme learning machine (ELM). The methods' performance in mapping input data to the output were compared. The mean regression errors calculated by the curve fitting model, ANN, NLR and ELM are obtained as 2.5, 8.0, 11.25 and 0.8 %, respectively. The experimental results show that ELM's nonlinear system modeling capability is superior to ANN, NLR, and CF.