A fuel pump includes a housing provided with an axial bore defining a compression chamber. The pump is further provided with a cylindrical piston slidably arranged in the bore, the piston extending from a top extremity that is inside the bore, defining a high pressure extremity, to a lower extremity, defining a low pressure extremity. The piston is able to reciprocally slide between a lower position where fuel at low pressure enters the compression chamber via an inlet and, a top position where fuel present in the compression chamber is pressurized before being expelled via an outlet. The piston is also provided with a recess surrounded by a peripheral wall arranged on its high pressure extremity, the recess and peripheral wall enabling the piston to expand radially when fuel in the compression chamber is pressurized.