Since liquid tank systems are commonly used in industrial applications, system-related requirements results in many modeling and control problems because of their interactive use with other process control elements. Modeling stage is one of the most noteworthy parts in the design of a control system. Although nonlinear tank problems have been widely addressed in classical system dynamics, when designing intelligent control systems, the corresponding model for simulation should reflect the whole characteristics of the real system to be controlled. In this study, a coupled, interacting, nonlinear liquid leveling tank system is modeled using ANFIS (Adaptive-Network-Based Fuzzy Inference System), which will be further used to design and apply a fuzzy-PID control to this system. Firstly, mathematical modeling of the system is established and then, data gathered from this model is employed to create an ANFIS model of the system. Both mathematical and ANFIS model is compared, model consistencies are discussed, and flexibility of ANFIS modeling is shown.