Firstly, sample square-circular transition tube along straight central route was modeled on CATIA software. The parameters are as follows： let the tube length is L, and the constant cross section area is S, and S = πR^2 = a2, in which R stands for the circle radius on one end, and a the square side length on the other end; set up the coordinate system with OX axis on the central route in which the origin O is on centroid of the square end and assume the cross section size at x as the square shaped with all four comers filleted in radius r which is proportional to x, that is, the linear slope of r is R/L, thus, both values r and square side length ax can be attained on the constant cross section area assumption. Secondly, some sample polygonal-circular transition tubes along straight, circular and helical central route were implemented similarly. Thirdly, numerical analysis of stress and displacement of these tubes were carried out on MSC/PATRAN software which are important to the distribution of turbulent flow and the layout of these transitional tube structures.