An elevator car arrangement includes an elevator car body and an elevator car sling. The elevator car arrangement further includes a hanging damper arranged to connect the elevator car body and the elevator car sling together for dampening vibrations coming from guide rails through the elevator car sling to the elevator car body. The hanging damper includes a first part connected to a bottom part of the elevator car body; a second part connected to the elevator car sling; and a damping element arranged to dampen vibrations coming from the second part to the first part. A method for dampening vibrations coming from guide rails through the elevator car sling to the elevator car body is disclosed.