Days When Fasting Is Prohibited

'In total there are five days when fasting is Haraam (forbidden). They are the days of Eidul Fitr (1st of Shawwal), and the 10th (Eidul Adha), 11th, 12th, and 13th of Dhul Hijjah. These four days of Dhul Hijjah are called Ayaamut Tashreeq (the days of Tashreeq). 

A Hadeeth is narrated in Bukhari (Vol.1, p267) from Hadhrat Abu Moosa (radiallahu 'anh), as well as Hadhrat Abu Huraira (radiallahu 'anh) that Rasulullaah (sallallahu 'alayhi wa sallam) prohibited fasting on the days of Eidul Fitr (1st of Shawwal) and Eidul Adha (10th of Dhull Hijjah). (Tafseer Anwaar ul Bayaan) 


Courtesy: http://www.muftisays.com/blog/Seifeddine-M/1986_26-08-2011/fasting-in-shawwal.html