PURPOSE: To manufacture Tee fittings advantageous in strength, by performing an upsetting work of a flat blank pipe in its axial direction with a pair of eccentric dies to form both the end parts into circular ones while drawing them eccentrically to the central part of said pipe.

CONSTITUTION: A flattening work of a circular blank pipe having the diameter larger than that of a product mother pipe is performed until the dia. of the blank pipe becomes equal to the diameter D0 of the product mother pipe. This flat blank pipe 7', of which both the end parts II' and II' are heated leaving the central partI' of the pipe 7' having the width approximately equal to the dia. d0 of a branch pipe as shown by the oblique lines without heated, is set to a pair of eccentric dies 20 and 20 after said heating. Next, the blank pipe 7' is upsetted into the dies 20 and 20 by approaching the dies 20 and 20 to each other. By this upsetting, the central partI' remains without causing a deformation, and only both the end parts II' and II' of high temperature are drawn into circular shapes while being drawn eccentrically to the side of major axis of the part 28 of the obtained eccentrically drawn pipe 24 by performing an usual diameter work, and a primary hole is drilled at the center of the expanded part to form a branch pipe by a conventional method. Thus the Tee fittings advantageous in strength are manufactured.