A method comprises in sequence the steps of: dispensing a continuous polymeric extrudate in a molten state; separating from the continuous extrudate a dose substantially having the shape of a parallelepiped, the dose having a separation surface at which the dose has been separated from the continuous extrudate, the dose further having a face adjacent to the separation surface; conveying the dose towards a mould comprising a first mould part and a second mould part; shaping the dose in the mould by moving the first mould part and the second mould part one towards the other in a moulding direction arranged transversally to said face, thereby obtaining a dispensing part of a container. The dispensing part comprises: an edge zone suitable for being joined to a container body; a neck surrounding a passage through which a product contained in the container can be dispensed; a membrane which closes the passage, the passage being intended to be opened after the shaping step, so that said product can flow out.