Sa’i may be performed either riding or walking, but walking is preferable. In the hadith narrated by Ibn ‘Abbas we find that the Prophet (peace be upon him) performed Sa’i on foot, but when the overcrowding increased and he found that the people wanted to know more (about their religion), he rode his mount so that they could see him and ask him (whatever they wanted to ask).
Abu At-Tufail asked Ibn ‘Abbas, “Tell me about the Sa’i between Safa and Marwah – is it (really) sunnah to perform it riding, for your people claim it is?” Ibn ‘Abbas replied, “They are right, but they are wrong.” Then he added, “The people crowded around the Prophet (peace be upon him), saying ‘This is (Prophet) Muhammad, this is (Prophet) Muhammad. Even young girls came out of their houses to see him. So when the people overcrowded he mounted on his camel, because the people were not beaten back (to make way for the Prophet).”
Muslim reported that walking in Sa’i is better, and riding, though permitted, is disliked. Tirmizhi has reported that a group of knowledgeable people disliked that someone should perform tawaf of the House and make Sa’i between Safa and Marwah riding on a mount without any genuine excuse. This is the opinion of Ash-Shafi’i.
The Malikites hold that a person who performs Sa’i between Safa and Marwah riding without any genuine reason, must repeat it, if there is still time for him to do so. And if there is no time, then he must offer a sacrifice in penalty, because it is wajib (obligatory) for him if he is able to walk. Abu Hanifah holds a similar view. According to these scholars the Prophet (peace be upon him) performed the Sa’i riding because of the large number of people around him.