Composite pipes have been utilized in the petrochemical industries where corrosion resistance and light weight are important. There is a need to calculate the buckling load for the pipe under torsion which develops from the structural loadings. An analytical model of composite pipe in torsion is developed during this study. Laminated anisotropic plate theory is utilized to derive the kinematics and constitutive relations of the pipe wall laminates. Solutions are obtained by using the Ritz method with suitable boundary conditions. Good agreement is found when comparing the present results with the analytical and experimental results from previous research.