When a weld area of weld surface between a flange portion 3a of a pipe 3 and a flange portion 4a of a pipe connection member 4 is S and total energy consumed on the weld surface is Et, ultrasonic welding is carried out to produce said ultrasonic weld assembly in such a manner that an energy density E defined as the quotient obtained by dividing the total energy Et by the weld area S satisfies the relation 26.69e.sup.-0.3708P