The present invention relates to a tube having a dispensing head and a flexible skirt. The skirt and the dispensing head include a single wall manufactured in a single injection-molding operation in an injection mold. According to the invention, the wall is made of a material whose base constituent is a high-density polyethylene (HDPE) or a mixture of polymers, at least one of which is a high-density polyethylene representing from 5% to 100% by weight of the polymers constituting the wall. The present invention also relates to a process for manufacturing such a tube.