1)    From the beginning of the month of Sivan up to and including the day after Shavuos we do not say Tachanun, as on the second day of Sivan Moshe warned the people to sanctify themselves and prepare themselves for the giving of the Torah. This was followed by the three days of the boundaries around the mountain, and then the festival and the day following. (Shulchan Aruch and Mishne Berurah 494)

2)    There are some who do not say Tachanun until the thirteenth day of Sivan since these days are days when one still bring the offerings of the festival if one did not bring them on the festival itself. (Kaf Hachaim ibid)