The fully developed laminar flow in helical elliptical pipes is influenced by curvature, torsion and aspect ratio of cross-section. With the aid of the symbolic manipulation technique, the governing equations were solved by the Galerkin method. The procedures of implementing the Galerkin method for flows in curvilinear pipes were discussed. The effects of the aspect ratio and torsion on the flow structure, wall shear stress and flow ratio were examined in detail. The results show that the flow characteristic for aspect ratio larger than unit is quite different from those for the aspect ratio smaller than unit.