A bottomed cylindrical member is disposed inner side of a stator core and a coil. The cylindrical member is made of non-magnetic material such as a stainless steel. The cylindrical member has a small diameter portion at the bottom side and a large diameter portion continuously made with the small diameter portion at the side of an attracting portion and has a larger inner diameter than that of the small diameter portion. The small diameter portion is slidablly in contact with a slider core, and reciprocatably supports the slider core. Since a radius difference between the small diameter portion and the large diameter portion is equal to or larger than 30 μm, a clearance larger than sliding clearance is formed between an inner circumferential surface of the large diameter portion and an outer circumferential surface of the sliding core. Thus, an electromagnetic driving apparatus and an electromagnetic valve, which smoothly reciprocate the sliding core, are provided.