The Days of Tashreeq are the three days following `Eid Al-Adha (Dhul-Hijjah 11–13). The Prophet (peace and blessings be upon him) said, “The Days of Tashreeq are days of eating, drinking, and remembering Allah” (Muslim). He did not allow anyone to fast on these three days except for the pilgrims performing tamattu` or qiran who did not have a sacrificial animal with them. It was narrated that `A’ishah and Ibn `Umar (may Allah be pleased with them) said, “No one was allowed to fast on the Days of Tashreeq except one who could not find a hadi (sacrificial animal)” (Al-Bukhari).
Sheikh Abdul-`Aziz ibn Baz, the late Mufti of Saudi Arabia stated that: Fasting should not be observed on the day of `Eid Al-Adha or the Days of Tashreeq because the Messenger of Allah (peace and blessings be upon him) forbade that. There is, however, evidence that it is permissible to fast on the Days of Tashreeq for the pilgrim performing tamattu` or qiran Hajj in lieu of offering the sacrifice, especially those who are unable to offer the sacrifice. But fasting these days on a voluntary basis or for any other reason is not permissible, as in the case of `Eid.
The late Sheikh I0bn `Uthaymeen, a prominent Saudi Muslim scholar, (may Allah have mercy on his soul) adds:
It is permissible for those who are doing Hajj qiran or tamattu`, if they cannot find a hadi, to fast these three days so that the Hajj season will not end before they fast. But apart from that, it is not permissible to fast on these days, even if a person is obliged to fast for two consecutive months; he should not fast on the day of `Eid and the three days following it, but then he should continue his fast. Based on this, the fasts that you observed on these days to make up for the days of fasting you missed in Ramadan are not valid, and you must repeat them.
When making up for the days of fasting you missed in Ramadan, you need not fast on consecutive days.