A high pressure isostatic pressing assembly , in particular food high pressure processing assembly, comprising at least one high pressure, longitudinal vessel having an internal chamber closed at both axial ends with two head assemblies , each comprising a body adjoining the vessel , wherein at least one head assembly further comprises a blocking chamber located within the body transversely relative to the longitudinal axis (A) of the vessel , a loading outlet , substantially aligned with the axis (A) of the vessel , joining an axially external side of the body with said blocking chamber , and having cross-sectional area substantially corresponding to the cross-sectional area of the vessel , and a plug disposed displaceably within the blocking chamber and provided with a sealing means apt to enter and sealingly close the internal chamber of the vessel during the pressure applying phase of the vessel , characterized in that it further comprises at least two longitudinal tie-rods juxtaposed, preferably symmetrically, around the external surface of the vessel at the radially external side of the blocking chamber , wherein each end of each tie rod passes through a tie member , coupled with the vessel , and is coupled with a resisting surface transferring axial load on said tie member at the axially external side of said end of said tie rod , wherein said resisting surfaces axially preload said tie-rod , said body and said vessel , and the preload force is adjusted at least to the value ensuring that no separation between said body and said vessel occurs during the loading and closing phase of the vessel , as well as during the pressure applying phase of the vessel so that the vessel is axially compressed in all the range of pressures acting inside the vessel by the head assemblies coupled with the tie-rods . at least one head assembly further comprises a blocking chamber located within the body transversely relative to the longitudinal axis (A) of the vessel , a loading outlet , substantially aligned with the axis (A) of the vessel , joining an axially external side of the body with said blocking chamber , and having cross-sectional area substantially corresponding to the cross-sectional area of the vessel , and a plug disposed displaceably within the blocking chamber and provided with a sealing means apt to enter and sealingly close the internal chamber of the vessel during the pressure applying phase of the vessel , characterized in that it further comprises at least two longitudinal tie-rods juxtaposed, preferably symmetrically, around the external surface of the vessel at the radially external side of the blocking chamber , wherein each end of each tie rod passes through a tie member , coupled with the vessel , and is coupled with a resisting surface transferring axial load on said tie member at the axially external side of said end of said tie rod , wherein said resisting surfaces axially preload said tie-rod , said body and said vessel , and the preload force is adjusted at least to the value ensuring that no separation between said body and said vessel occurs during the loading and closing phase of the vessel , as well as during the pressure applying phase of the vessel so that the vessel is axially compressed in all the range of pressures acting inside the vessel by the head assemblies coupled with the tie-rods . <EOS>