Abstract: Method of manufacturing an acute angled vessel connector adapted to be mounted in a vessel or pipeline and to provide an angled connection from such vessel or pipeline to a branch pipe wherein the vessel connector includes a generally cylindrical main body having integrally formed therewith a contoured mounting rim, the main body having a bore therethrough which is directed at a pre-designated acute angle with respect to the annular mounting rim wherein the method includes the steps of providing an offset forging of a particular shape, machining an interior body bore on a central axis separate from the longitudinal axis of the forging itself, facing one end of the forging and milling the other end with a curved undersurface of the same radius of curvature of the vessel or pipeline in which the connector is to be mounted and thereafter completing the machining of the outside surface and otherwise forming the contoured mounting rim of a generally elliptical shape.