Blanks which are made of cardboard or the like and wherein the neighboring panels are flexible relative to each other are converted first into flat tubular preforms which are thereupon expanded prior to a change of orientation and introduction into a filling machine. The conversion is carried out on a horizontal support during stepwise transport of successive blanks along a stationary elongated one-piece flat pattern having progressively narrower portions at several successive deforming stations. At the first deforming station, a lap which is integral with one outermost panel of each blank is flexed relative to the respective outermost panel; at the second deforming station, the lap and the respective outermost panel are folded over the adjacent portion of the pattern; and the other outermost panel is bonded to the lap at the third deforming station. The width of the pattern at the first deforming station equals the combined width of three neighboring panels, and the width of the pattern at the second and third deforming stations equals the combined width of two neighboring panels. The thus obtained flat tubular preforms are expanded at an additional station where the width of the pattern equals the width of a single panel.