In The Name of Allaah, The Most Merciful, The Bestower of Mercy
Ayyaam An-Nahr (i.e. the days of sacrifice/slaughtering) are four:  The day of Eed and  The three days after that.
According to Imaam Muhammad Bin Saaleh al-Uthaymeen (rahimahullaah) the Eed sacrifice is a Sunnah Mu-akkadah [i.e. the Prophet (sallal-laahu-alayhi-wasallam) performed it continuously, but did not make it an obligation)].
The Eed sacrifice is only legislated for those who are alive. It is neither reported from the Prophet (sallal-laahu-alayhi-wasallam) nor from his companions (radiyallaahu-anhum) that they exclusively slaughtered on behalf of the dead, rather men used to slaughter the Eed sacrifice for their households. [For further clarification, see article on this link: http://salaficentre.com/2012/10/rulings-regarding-the-slaughtering-sh-ibn-baz-and-sh-ibn-ul-uthaymeen/]
Conditions to be fulfilled:
Firstly: The animal to be slaughtered has to be a camel and other cattle (such as sheep, goat). If a horse is slaughtered, it will not be accepted; because it is not from those types of animals to be slaughtered for the Eed sacrifice. The evidence for this is the statement of the Messenger (sallal-laahu-alayhi-wasallam): ‘’whoever performs an action that is not from this affair of ours (i.e. the Qur’an and the Sunnah) will have it rejected’’
Secondly: The animal has to be a particular age: Sheep: It should be at least six months old. Cow: It should be at least two years old. Camel: It should be at least five years old.
Thirdly: The animal should be free from obvious defects. The Messenger (sallal-laahu-alayhi-wasallam) said: There are four (animals) that cannot be offered as sacrifice:  The one-eyed animal whose defect is clearly visible;  a sick animal whose sickness is clearly visible;  a disabled animal whose disability is clearly visible;  an emaciated animal that has no fat around its bones (i.e. due to illness)’’
Fourthly: The Eed sacrifice should be offered after the Eed salaah and within the days of Eed (i.e. the days of Eed are the day of the prayer and the consecutive three days after it)
The one who intends to offer the Eed sacrifice should not remove any of his bodily hair until after the slaughtering. And concerning the opinion that the one slaughtering on behalf of someone is like the one that deputised him and he is also not to remove any of his bodily hair, then this opinion is weak; because the Messenger (sallal-laahu-alayhi-wasallam) said: ‘’When you sight the new moon of Dhul Hijjah, and if anyone of you wishes to offer the sacrifice, then he should not remove anything from his hair or nails until he has offered his sacrifice;’’ but he (sallal-laahu-alayhi-wasallam) did not say: ‘’Or the one who slaughters on his behalf’’
To be continued……Inshaa-Allaah
This article was paraphrased from an article posted at www.sahab.net: see link: http://www.sahab.net/forums/index.php?showtopic=132870
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