Yahya related to me from Malik from Nafi that Abdullah ibn Umarused to do tayammum up to his elbows.Malik was asked abouthow tayammum was done and what parts were covered and he said, "Strikethe ground once for the face and once for the arms and wipe them tothe elbows."
USC-MSA web (English) reference: Book 2, Hadith 93
Arabic reference: Book 2, Hadith 123