Abstract: A method and associated apparatus for lateral drilling in an oil and/or gas well involving either stopping the drilling or temporarily cementing in a plug in the existing well bore at the desired location for deviation. A tight radius of curvature is then rotary drilled by use of a flexible drilling collar made up of a series of short drill string sections interconnected by universal joints that terminate within an eccentric collar on the final drill string section. The eccentric collar is equipped with a sidewall engaging means to hold the eccentric collar from rotating during rotary drilling. A flexible collar (e.g., ball and socket) extending outwardly and downwardly from the far end of the final drill string section passing through the eccentric collar connects to a drill bit collar and rotary drill bit.