The Messenger of Allah (ﷺ) said: Going round the House (the Ka'bah), running between as-Safa and lapidation of the pillars are meant for the remembrance of Allah.
Sunan Abi Dawud Book 11, Hadith 168
← Previous Hadith I heard Umar ibn al-Khattab say: What is the need of walking proudly (ramal) and moving the shoulders (while going round the Ka'bah)? Allah has now strengthened Islam and obliterated disbelief and the infidels. In spite of that we shall not forsake anything that we used to do during the time of the Messenger of Allah (ﷺ).

Sunan Abi Dawud Book 11, Hadith 167 Next Hadith → The Prophet (ﷺ) wore the mantle under his right armpit with the end over his left shoulder, and touched the corner (Black Stone), then uttered "Allah is most great" and walked proudly in three circuits of circumambulation. When they (the Companions) reached the Yamani corner, and disappeared from the eyes of the Quraysh, they walked as usual; When they appeared before them, they walked proudly with rapid strides. Thereupon the Quraysh said: They look to be the deer (that are jumping). Ibn Abbas said: Hence this became the sunnah (model behaviour of the Prophet).

Sunan Abi Dawud Book 11, Hadith 169