To provide an electrically driven power steering apparatus with a simple structure, which can prevent overloading of an electrical motor and a power transmission system, an absorbing member (121) is attached to a rack shaft (112), and is brought into contact with a rack housing face at a stroke end of the rack shaft (112). The absorbing member (121) at least partially has a material having a Young's modulus of 100 to 900 Mpa, and thus it is possible to effectively relieve an impact at the stroke end.