Our elbow element presented in an earlier communication is enhanced to account for interaction effects between elbows and rigid flanges, elbows of different curvatures, and elbows joining straight pipe sections. The interaction effects are modeled by including the appropriate additional strain terms in the stiffness matrix formulation and by using a penalty procedure to enforce the continuity of the derivatives in the pipe skin radial displacements. The enhancement in the formulation has been implemented and the results of various sample analyses are presented.