A container handling machine including at least one operative unit comprising support means to support a shaped container, and a plunger selectively moved along a given axis to deform a base of the container from a first swollen configuration to a second configuration, in which the base is in part retracted inwardly of the container with respect to the first configuration so as to form a recess delimited by a boundary surface defining an internal volume of the container smaller than that in the first configuration. The plunger is provided with a shaped head interacting with the container base and comprising: first engaging means and an interacting surface.