The invention relates to an unbonded flexible pipe with a length and a longitudinal axis. The pipe comprises an inner sealing sheath defining a bore, a pressure armor layer, an intermediate sealing sheath and a tensile armor. The pressure armor layer comprises at least one elongate metal element arranged with pressure armor gaps and is arranged in an annulus provided between the inner sealing sheath and the intermediate sealing sheath. The tensile armor is arranged on the outer side of the intermediate sealing sheath. Either the intermediate sealing sheath forms a drainage layer or the unbonded flexible pipe further comprises a drainage layer arranged in the annulus. The drainage layer comprises at least one drainage path arranged along the length of the pipe, wherein the drainage path is in fluid communication with the pressure armor gaps. The drainage layer optionally comprises a perforated tube.