There are provided a sheet feeding apparatus which, with a simple configuration, can suppress generation of noise during feeding of a sheet without having an affect on sheet separating performance, and an image forming apparatus which includes this sheet feeding apparatus. The sheet feeding apparatus includes: a feeding roller which feeds a sheet S; a separation roller which is pressed against the feeding roller and rotates in a reverse direction to a direction of feeding by the feeding roller to separate sheets, fed by the sheet feeding apparatus, one by one; a feeding rotational shaft which transmits rotational driving force to the feeding roller; and a roller dumper which is provided between the feeding roller and the feeding rotational shaft, and transmits the rotational driving force from the feeding rotational shaft to the feeding roller, while absorbing vibrations of the feeding roller.