A pump head for a fuel pump for use in a common rail fuel injection system, the pump head (100; 200; 300) comprising: a pump head housing (102; 202; 302); a pumping chamber (106; 206; 306) defined within the pump head housing (102; 202; 302); and an inlet valve arrangement (108; 208; 308) for controlling fuel flow into the pumping chamber (106; 206; 306), the inlet valve arrangement (108; 208; 308) including an inlet valve member (110; 210; 310) moveable between open and closed positions characterized in that the pump head is further provided with means of viscoelastic damping ensuring that, in use, movement of the inlet valve member (110; 210; 310) is damped when moving into the open position and also, when moving into the closed position, the pump head further comprising a damping volume (156; 256; 356) which is defined, at least in part, by a surface associated with the inlet valve member (110; 210; 310) such that, in use, the size of the damping volume (156; 256; 356) varies in response to movement of the inlet valve member (110; 210; 310) and, viscoelastic damping of the inlet valve member (110; 210; 310) is effected by the restricted flow of fuel between the damping volume (156; 256; 356) and a second volume and wherein the second volume is a chamber (142; 242; 342) disposed externally to the pump head housing (102; 202; 302), the damping volume (156; 256; 356) being in fluid communication with the external chamber (142; 242; 342) and wherein the inlet valve member (110; 210) comprises an elongate neck (114; 214) which is guided within a valve bore (118; 218) in the pump head housing (102; 202), the valve bore (118; 218) extending between an upper surface (120; 220) of the pump head housing (102; 202) and a valve seat (130; 230); wherein the external chamber (142; 242) is defined between the closure member (134; 234) and the upper surface (120; 220) of the pump head housing (102; 202); wherein a distal end (124; 224) of the neck (114; 214), disposed away from the valve seat (130; 230), projects above the upper surface (120; 220) of the pump head housing (102; 202) into the external chamber (142; 242); and wherein the damping volume (156; 256) is defined, at least in part, between a radial outer surface of the distal end (124; 224) of the neck (114; 214) and the radial inner surface of an annular shroud (152; 252) disposed around the distal end (124; 224) of the neck (114; 214). a pump head housing (102; 202; 302); a pumping chamber (106; 206; 306) defined within the pump head housing (102; 202; 302); and an inlet valve arrangement (108; 208; 308) for controlling fuel flow into the pumping chamber (106; 206; 306), the inlet valve arrangement (108; 208; 308) including an inlet valve member (110; 210; 310) moveable between open and closed positions characterized in that the pump head is further provided with means of viscoelastic damping ensuring that, in use, movement of the inlet valve member (110; 210; 310) is damped when moving into the open position and also, when moving into the closed position, the pump head further comprising a damping volume (156; 256; 356) which is defined, at least in part, by a surface associated with the inlet valve member (110; 210; 310) such that, in use, the size of the damping volume (156; 256; 356) varies in response to movement of the inlet valve member (110; 210; 310) and, viscoelastic damping of the inlet valve member (110; 210; 310) is effected by the restricted flow of fuel between the damping volume (156; 256; 356) and a second volume and wherein the second volume is a chamber (142; 242; 342) disposed externally to the pump head housing (102; 202; 302), the damping volume (156; 256; 356) being in fluid communication with the external chamber (142; 242; 342) and wherein the inlet valve member (110; 210) comprises an elongate neck (114; 214) which is guided within a valve bore (118; 218) in the pump head housing (102; 202), the valve bore (118; 218) extending between an upper surface (120; 220) of the pump head housing (102; 202) and a valve seat (130; 230); wherein the external chamber (142; 242) is defined between the closure member (134; 234) and the upper surface (120; 220) of the pump head housing (102; 202); wherein a distal end (124; 224) of the neck (114; 214), disposed away from the valve seat (130; 230), projects above the upper surface (120; 220) of the pump head housing (102; 202) into the external chamber (142; 242); and wherein the damping volume (156; 256) is defined, at least in part, between a radial outer surface of the distal end (124; 224) of the neck (114; 214) and the radial inner surface of an annular shroud (152; 252) disposed around the distal end (124; 224) of the neck (114; 214).