PURPOSE: To save a labor by reducing the executing man/hour at connection time by giving a mechanical force by outer-inserting the connection pipe forming the excess metal part plastically deformable the pipe end part of the tubular body to be connected.

CONSTITUTION: The elbow 3 having the pipe end part whose diameter is expanded to the inner bore about equal to the outer bore dimension of a tubular body 2 is outer-inserted with its adhesion to the pipe end part of both steel pipes 2, 2 in an equal bore. Plural excess metal parts 3a of annular projections in rectangular section projecting to the external part in the radial direction are formed on the outer periphery close to both end parts of this elbow 3, which is composed of a plastically deformable material. For instance the die 4 of a split die is located so that its tapered face 4a may approach to the excess metal part 3a and a anchor 7 is stationarily located in the zone transferring to the diameter expanding part of the elbow 3 to forcibly move the die 4 in the axial direction by a driving means. As a result the plastic deformation to the inner part in the radial direction is caused on the corresponding part to the excess metal part 3a of a thin tubular body 2 as well according to the excess metal part 3a being deformed to the inner part in the radial direction and the part 3 is adhesively bitten to the deformed part of the tubular body 2.