Curved or twisted tube is important in generating cross-stream secondary flow and increased degree of mixing. In the present paper, laminar fluid flow and heat transfer is analyzed for twisted elliptic tubes by using a finite difference method. Fully-developed flow is assumed, and the thermal conditions of axially uniform wall heat flux and circum-ferentially constant temperature at an axial position are used. The solution domain or the inner region of an ellipse is transformed to a rectangular computational domain by using a new, simple analytic transformation fitting the boundary exactly. The parametric effect of the twist rate of the pipe and the aspect ratio of the cross-sectional ellipse is investigated in terms of flow structures and Nusselt numbers.