The increased usage of fiber reinforced plastic (FRP) composite pressure vessels and piping components in the past decades in the residential and industrial sectors is attributed to the FRP material resistance to corrosion and chemical attacks. FRP composite flanges are, however, known for their anisotropic behavior. In the ASME code section X, FRP composite flanges are treated using an analytical approach derived from that metallic flanges in addition to the fact that the geometries are made to fit them as much as possible and not designed independently. This is known to have caused structural flaws for certain FRP flange classes and sizes. Using a recently developed anisotropic FRP flange approach, it is proposed to identify the most critical flanges by analyzing the flange parameters such as flange ring rotation and stresses in their different parts; gasket, flange ring, hub, and shell subjected to pressure loading. The study on the strength of flanges described in ASME section X RD-620.1 table, will reveal the most critical size and class flanges and their highly stressed locations. To conduct such a study, the selected flange material is an E glass/Vinyl Ester laminate composite. The study shows that FRP flanges of classes 25 and 50 are most vulnerable and should comparatively be less loaded. The stresses are found to reach 50 MPa in the shell and 58 MPa in the flange ring while the maximum flange rotation is 0.83 deg.