The invention relates to a method and apparatus for shaping an elongated glass body 81, which is a glass tube or glass rod and has an initial profile, to an elongated glass body having a different profile. In order to be properly shaped, an elongated glass body 81 passes through, in a hot malleable state, a nip, which is formed by squeezing rollers 1 and which has a nip width which is less than an outer dimension of the initial profile.In order to accomplish an enhanced precision of the shaping process, according to the invention the position of at least one of the squeezing rollers is varied continuously so that a contact area between the respective squeezing roller and the hot glass body is varied cyclic reciprocating movement. Disturbing effects such as local overheating of the squeezing rollers or an accumulation of dirt or glass particles on the surface of the squeezing rollers can thus be effectively prevented.