When we refer to the Hadiths [i.e. narrations] of the Ahl al-Bayt (as) we come across two types of narrations that can be used to confirm the fact that not only is it allowed to read the chapters of the holy Quran on behalf of the deceased, but also it is highly recommended and of great benefit to them.
The first type of narrations are the ones which generally suggest that we should remember the dead and that they benefit from and are greatly in need of the good deeds that we might perform on their behalf, and there is no doubt that reciting the Quran is a perfect example of the good deeds one can ever perform.
In this vein, the prophet (s) is reported to have said,
Do not forget your deceased ones who rest in the graves; they [desperately] expect your favours; They are like prisoners and are in need of your help; they no longer have the chance to do anything good, but you can do charitable acts [on their behalf] and pray for them. 1
The second type of narrations are the ones which specifically mention what verses we can read and what effects and benefits are brought about by reciting such verses. For example, Imam al-Riza (as) is reported to have said,
Whoever pays a visit to the grave of a deceased person and recites the chapter of al-Qadr seven times, Allah will forgive the sins of the deceased person as well as those of the visitor who recited the verses. 2
In another narration, it is stated,
One who visits a cemetery and recites the chapter of Yaseen granting its reward to all those buried therein, Allah will alleviate their chastisement on that day and will also give rewards to the reciter equal to the number of those buried in that cemetery. 3
We can conclude by saying that many of those of our family members and relatives and even our friends who have passed away are desperately waiting for us to have mercy on them by remembering them, seeking forgiveness for them and performing good deeds on their behalf, so that Allah might bestow His mercy and forgiveness upon them, overlook their mistakes and sins and raise them with the righteous.
---------------------------
1. Anwar al-Hidaya, p. 115
2. Bihar al-Anwar, vol. 79, p. 169
3. 'Uddat al-Da'ee, p. 146
One of the manifestations of Allah's mercy towards his servants is the fact that He has allowed the deceased to benefit from the good deeds done on their behalf by those who are alive. Now one might ask whether it is considered a good deed to recite the Quran and grant its reward as a gift to those who have died and have lost the opportunity to do any good themselves...