Public display of grief is not allowed on the Sabbath and Jewish Holidays: Rosh HaShanah / ראש השנה, Yom Kippur / יום כפור, Succoth / סוכות, Passover / פסח and Shavuot / שבועות.
Jewish Holidays. The positive scriptural commandment in the Book of Deuteronomy 16:14“and you shall rejoice on your festival / ושמחת בחגך”, directed towards the entire Jewish people, supercedes the rabbinical commandment of mourning for individuals (Talmud, Tractate Moed Katan 14b). Therefore, the above-mentioned scripturally mandated Jewish Holidays terminate Shivah / שבעה even if it was observed only for a fraction of a day. If Shiva was not observed at all as, for example, when the burial was on Chol HaMoed / חול המועד — intermediate days of the festival, it is postponed until after the conclusion of the festival. In such a case, the second day of Rosh HaShanah / ראש השנה and, in the Diaspora, the second day of a closing Yom Tov / יום טוב of any festival, is counted as the first day of the Shivah, even though no mourning is observed on that day.
The Sabbath, on the other hand, does not terminate Shiva. Otherwise, it would never be possible to observe Shivah for a full seven days. The Sabbath only suspends the public display of grief (Avelut SheBePharhesia / אבלות שבפרהסיא) requiring the mourners to observe those mourning practices that are by nature private and inconspicuous (Avelut SheBeTzina / אבלות שבצינעה). Thus, the mourners are allowed to exchange greetings, sit on regular chairs, wear regular shoes and change garments that were torn as a sign of mourning during the funeral, as explained in the section about Keriah / קריעה — rending of garments. Private mourning continues, however, and therefore playing games, using cosmetics, washing oneself for pleasure, marital intimacy, reading books and newspapers and Torah study are not allowed even on the Sabbath. However, some rabbinical authorities allow reviewing the weekly Torah Portion, i.e., reading it twice in the original Hebrew and once in the Aramaic translation, as well as reading Rashi's / רש"י commentary. Since some of the mourning practices are observed on the Sabbath, it is counted as one of the Shiva days.
Many rabbinical authorities allow the mourners to start gradually relaxing mourning related restrictions on Friday afternoon in preparation for the Sabbath. Preparations do not include, however, taking a shower, haircut, shaving, etc.
It is customary that the mourners do not leave their home even on the Sabbath except to go to the synagogue. On Friday night they usually join the congregation right after Kabbalat Shabbat / קבלת שבת — greeting of the Sabbath ceremony, prior to reciting Psalm 92. Mourners omit certain parts of the Sabbath prayers and ceremonies, depending on the local custom. In many congregations the second chapter of the Mishnah / משנה, Tractate Shabbat is recited on the Sabbath as part of the Evening Prayer Service. The mourners skip it. After returning home they neither recite the “Shalom Aleichem / שלום עליכם” hymn nor bless their children on the Sabbath Eve. They do sing Zemirot / זמירות — songs during the Sabbath meals, however. Mourners do not lead the service and are not called up to the public Torah reading in the synagogue. Unless there is no substitute, they should not perform the Torah reading either.
At the conclusion of the Sabbath, mourners resume their mourning. Leather shoes are usually removed right before the Evening Prayer Service. Psalm 49, which is normally recited in some communities after the Evening Prayer Service in the house of mourning, is substituted with Psalms 16 after the Sabbath. If the mourner recites Havdalah / הבדלה — he skips the joyous introductory verses and proceeds directly to the blessing over wine. The mourner may recite Kiddush Levana / קידוש לבנה — sanctification of the Moon, if the opportunity will pass before the end of Shivah, but should not recite it together with a group of people. According to many rabbinical authorities, he should recite just the blessing and skip the Psalms and other additions, including the Shalom Aleichem / שלום עליכם greetings found in the prayer.
Purim and Chanukah. Public display of grief is not allowed on Purim / פורים and Shushan Purim / שושן פורים, but private mourning continues. Thus, both of these days are counted towards the required seven days of Shiva, even though no public mourning is observed. Mourners send only two gifts — Mishloach Manot / משלוח מנות, which is the minimum requirement on Purim. The mourners, however, should not send items associated with joy, such as wine, fancy foods, etc. The custom is not to send gifts to the mourners during Shivah.
On Chanukah / חנוכה the mourners light the candles and recite all the required blessings at home, but not in the synagogue. On Chanukah some communities have a custom to omit Hallel / הלל altogether in the house of mourning, while others require the mourners to step out of the room and then recite it. Sephardim, however, usually allow the mourners to recite Hallel / הלל with the blessing.