A fuel injection system for a reciprocating engine, comprising injectors for injecting pressurized fuel into the cylinders of the engine, a high pressure pump for pressurizing fuel to be injected, a supply pipe for feeding fuel from the high pressure pump toward the injectors and feed pipes for feeding fuel from the supply pipe to the injectors. The first ends of the feed pipes are connected to the injectors and the second ends to the supply pipe. Each fuel injector is provided with a pressure accumulator.