Sahih Muslim Book 7, Hadith Number 3089.

Chapter : One may perform Hajj on behalf of the maimed, the old and the deceased.

‘Abdullah b. ‘Abbas reported that while al-Fadl b. Abbas had been riding behind Allah’s Messenger (may peace be upon him) a women of the tribe of Khath’am came to him (to the Holy Prophet) asking for a religious verdict. Fadl looked at her and she looked at him. Allah’s Messenger (may peace be upon him) turned the face of al-Fadl to the other side. She said: Messenger of Allah, there is an obligation from Allah upon His servants in regard to Hajj. (But) my father is an aged man; he is incapable of riding safely. May I perform Hajj on his behalf? He said: Yes. It was during the Farewell Pilgrimage.