The method produces glass tubes having a predetermined inner profile according to a Vello-method or Down-Draw method, wherein molten glass emerges from an outlet orifice of a melt feed and is drawn over a shaping body to form a hollow drawing bulb, and the drawing bulb is drawn over a profile forming body downstream of the shaping body to form the predetermined inner profile. To enable a reliable, risk-free positioning of the profile forming body within the drawing bulb, the profile forming body is axially moved either from below the shaping body via an inner space of the glass tube or via an inner bore of a shaft supporting the shaping body until reaching an operational position in the inner space of the glass tube. An apparatus for performing the method is also described.