A method and apparatus for producing hollow articles made of injection moulded plastic material by a mould having a die within which there is inserted a core, and at least one injector including a pin valve displaceable between a closing position and an opening position for injecting the pressurized plastic material into a space comprised between the die and the core. During the injection, any flexural deflection of the core is detected and the pin valve of the or of each injector is displaced in a controlled fashion to adjust a pressure and a flow rate of the injected plastic material, so as to reduce or eliminate such deflection of the core.