Shavu‘ot, hebr. šābū‘ōt (‘weeks’) ‘Pentecost’, is an ancient feast of the first wheat harvest in Israel. During this feast the granting of Torah to Israel is commemorated, as well as sending of the Holy Ghost to G-d's people who accepted JHS as Messiah. It is celebrated on Sivan 6–7 in diaspora and on Sivan 6 in Israel.
However the Book of Jubilees (pre-masoretic Torah of the 2nd c. BC) puts Deut 16:9 and Lev 23:11 in agreement, in a way that Shavu‘ot can be treated as accomplishment of the Paschal Sabbath, i.e. as a “movable” feast celebrated on the FIRST DAY OF THE WEEK after the Sabbath of the finished 49 days omer-counting. This gives a messianic sense to the feast of Shavu‘ot, even deeper one than a traditional Day of sending the Holy Ghost to the Church: perfection of Rest on the Seventh day after the six days of Creation becomes fulfilled on the Eighth Day of coming Eternal Kingdom both in mutually irrelative Talmudic and early Christian eschatologies.
Thus Messiasnic Pesach starts on Nisan 14 as Day of the Atoning Sacrifice, but its Nisan 16, the Resurrection, manifests 7 weeks later on the Resurrection Day (Lord's First Day) of the week. This encourages Messianic Jews to celebrate Shavu‘ot on the first “Sunday” after the end of ‘omer-counting (or several days up to this date, starting from the traditional one as a compromise).

Entire symbolism of Torah-commanded feasts becomes clear only on the level of authentic Messianic Judaism, representing the whole process of G-d's Covenants. Traditional Rabbinic (Halachian) Judaism, positioning itself as a national religion of the Jews, is a fragment of Jewish history and a religion formed after the disappearance of the Temple Judaism. Today it pretends to represent the whole Judaism, however negating those who have not accepted the Oral Torah, but these are not only Messianic Jews, but also Qaraites. Enough to see that it resigned to Judeo-Christian Jews naming themselves messianic, although it should pretend to be messianic itself and only itself, since Messiah is a Figure unable to be removed from authentic Judaic faith. Even more: after many pseudo-messiahs first had been accepted but later negated by rabbinical Jews, this practically no more believable Figure became a symbol of a new religion which changed Torah commandments through commentaries making fulfilment of the commandments elective even in the most important case: that of purification with sacrifices. Thus the rabbinic (Orthodox) Messiah comes to restore the Temple while G-d has already brought the Jews home from exile. What a contrast to authentic Judaism of the time of coming back from the Babylonian captivity! Then the Jews came back first and foremost in order to rebuild the Temple and fulfil all commandments concerning Temple sacrifices! – In 1967 almost all rabbies of Israel asked Moshe Dayan to give keys of the Temple Mount to Moslems... This is essentially a new religion which cannot resolve all eschatologic enigmas of Torah including sense of the festivals.
On the other hand, the historic Christianity is even more uncapable to understand these enigmas, because it emerged as an Anti-Jewish Roman imperial ideology in 325 after having cursed all G-d's chosen people “scoundrels D-iciders”. Being in inner contraposition and permanently fracturing from the beginning (a result of the curse of 325 in accordance with Gen 12:3), it is a new religion in turn in comparison with authentic apostolic Judaism of the 1st c. The process of G-d's Covenants (Torah) has been replaced in it with canons and dogmas, G-d's commanded festivals have been replaced with invented new festivals but the Holy Text of Torah is used to support own doctrine, not as a living Word of G-d. Various “theologists” have lost any piety towards the Holy Text and treat it as a kind of archaic folklore. Israel as a people and as a country has been “replaced” by them with theirselves, so that the Jews have only one way for “salvation”: to adopt such “Christianity” and to stop being Jews.
However their regrettable fruits, when almost all former Christians have turned back to paganism today, show something antipodal: not the Jews should adopt this “Christainity”, but on the contrary, the last faithful Christians who want to save their souls, should come back to authentic apostolic Judaism.