Tachanun is omitted from the first of Sivan until after Shavuos. Our custom is to omit Tachanun until, and including, the 12th of Sivan. Tachanun is resumes on the 13th of Sivan. Likewise on Shabbos of these dates Av Harachamim and Tzidkascha Tzedek is omitted.
 494/8; Siddur Admur; Rama 494/3
The reason: The custom is to omit Tachanun from the beginning of Sivan until the 8th of Sivan. The reason for this is because starting from Chodesh Sivan, on each day before Matan Torah another preparation for Matan Torah occurred [and it is thus considered times of extra joy].
The following are the preparations:
- First of Sivan: No Tachanun as is Rosh Chodesh.
- Second of Sivan: The Jewish people were told “You will be for me a Mamleches Kohanim”
- Third of Sivan: The Jewish people were commanded the Mitzvah of Hagbala, to not enter into the vicinity of the mountain during Matan Torah.
- Fourth and Fifth of Sivan: The Jewish people were commanded the Mitzvah of separating from their wives.
- 6th and 7th day: Is Shavuos.
- 8th day: Is Issru Chag
 Siddur Admur
So also rules: Peri Chadash; Elya Raa 494/14; Shulchan Hatahor 131; Kaf Hachaim 494/52
Ruling of Shulchan Aruch Admur: In the Shulchan Aruch 494/8 Admur rules that Tachanun resumes on the 9th of Sivan [in the Diaspora]. So also rules: Rama 494/3
The reason-From the 8th-12th: According to the ruling in Shulchan Aruch ibid Tachanun is recited starting from the 9th of Sivan and onwards. However according to the Siddur, and so is our custom, Tachanun is omitted until, and including, the 12th of Sivan. The reason for this is because after Shavuos there is 7 days of Tashlumin for which the Holiday Karban is able to be sacrificed.
In Eretz Yisrael: According to the Shulchan Aruch, in Eretz Yisrael being that there is only one day of Yom Tov, Tachanun should resume on the 8th day of Sivan. However according to the Siddur we omit Tachanun until the 13th, and so is tehn custom in Eretz Yisrael. [Nitei Gavriel p. 221]