An injecting/blowing device includes a mold for injecting a thin-walled hollow preform capable of being transformed into a more voluminous hollow body. The mold includes a counter mold defining a cavity, a cure located in the cavity, and a preform impression located between the counter mold inner surface and the core which will receive the melt, at least two main preferential flow channels or at least two secondary preferential flow channels having a recessed zone at the surface of the core and the inner surface of the cavity. The main flow channels are located only at the impression zone corresponding to the zone for transforming the perform, and in the optional secondary flow channels are flow channels discontinuous from the main flow channel.