Y-branch is often used in connection between a main pipe and two branch pipes, for example, in furnace, quench boiler, nuclear parts and so on. The stress distribution in the Y-branch is very complicated because of complicated shape and complex loads on it. The stresses in the Y-branches cannot be determined by theoretical equations. Finite element method is used to analyze the stresses in the Y-branches. As an example, a Y-branch used in a high temperature furnace is calculated with ANSYS software. The temperature distribution and elastic and elastic-plastic stress fields in the Y-branch under mechanical and thermal loads are calculated. Strength, creep and fatigue of the Y-branch are evaluated based on T-1300, T-1400 of ASME Boiler and Pressure Vessel code Sec Ⅲ Div 1 Subsection NH.