Valves are important components in controlling the amount of fluid going to devices. One of these types is the butterfly valve (BFV) that adjusts the amount of flow by rotating the valve disk by means of its shafts which is usually located in the middle of the flow. Despite its common usage in various applications, the BFV is known to cause a high-pressure drop. Conversely, the pinch valve is another type of flow control device that uses a pinching mechanism to open and close the inner tube by pinching at different degrees. The absence of flow-controlling mechanisms in the flow path, such as the valve disk and its shaft, contribute to the minimal pressure drop in pinch valves. The high-pressure drop in BFVs and the minimal pressure drop in pinch valve flow make it worthwhile to investigate and compare their flow at all opening positions of the two valves. Therefore, this work numerically explores the potential of using the pinch valve as an alternative to the BFV in terms of its ability to attain a lower pressure loss, hence better flow rate. The influence of various BFV parameters such as shaft diameter, valve thickness, and valve disk edge were examined. The performance characteristics of both valves were obtained using CFD models formed on the SolidWorks program. This CFD model solves the differential equations using the finite element method. Moreover, a mathematical model to determine the area of the pinch valve at various pinching degrees was developed and compared with the results obtained from other mathematical models and CFD. It was shown that using a flat 1 mm valve disk thickness with round edges resulted in a 7.5% increase in mass flow rate compared to standard BFVs. On the other hand, using the pinch valve resulted in over a 700% mass flow rate compared to the BFV at a 25% opening position and a 49% increase in flow rate at a 75% opening position. Thus, the pinch valve has the potential to replace the BFV due to its better flow characteristics in any application.