Many people observe the custom to fast on a Yartzeit the anniversary of the passing of an immediate family member, particularly a parent. The question arises, if the Yartzeit happens to fall on Shabbat, Yom Tov, Rosh Hodesh, or other festive day when Halacha forbids fasting, should the fast be observed on a different day, and, if so, on which day?
Rav Shemuel Pinhasi (contemporary, Israel), in his work Haim Va'hesed (listen to audio recording for precise citation), records the different views that exist in this regard. He notes that whereas the Shulhan Aruch rules that in such a case the fast is observed on Sunday (or the day following the Yartzeit), the Rema (Rabbi Moshe Isserles, Poland, 1525-1572) maintains that one does not fast at all if the Yartzeit occurs on a day when fasting is forbidden. Others follow yet a third custom, namely, to observe the fast on Erev Shabbat, the day before the Yartzeit. Some authorities maintain that if the deceased had two or more sons, some sons should observe the fast on Friday while others fast on Sunday, in order to satisfy both opinions.
As for the final Halacha, Rav Pinhasi rules that when the Yartzeit falls on Shabbat the fast should be observed on Thursday, as it is inappropriate to fast on Erev Shabbat. However, if there are several brothers, then at least one brother should fast instead on Sunday, in accordance with the view of the Shulhan Aruch.
Needless to say, the Kaddish recitation, as well as the special Torah study sessions traditionally held on a Yartzeit, should take place on Shabbat, the actual date of the passing, even though the fast is observed on a different day.
Summary: Many people have the practice of fasting on a Yartzeit (anniversary of the passing of a family member), particularly for a parent. If the Yartzeit falls on Shabbat, then the fast is observed on Thursday; if there are two or more brothers, then some should fast on Thursday, and the others on Sunday. Even in such cases, the Kaddish recitation and special Torah study sessions take place on Shabbat.
