THE GEMARA GIVES A REASON WHY THE BERACHA OF "SIM SHALOM" IS AFTER "MODIM" BUT AS WE LEARNT IN BERACHOS THE TEFILLA IS DIVIDED INTO 3 "SHEVACH" "BAKASHA" AND HODAAH"
WHY IS "SIM SHALOAM " WHICH IS BAKASHA PLACED AFTER "MODIM?
Good question. The answer that I have heard is that the Bakashah for Shalom is different than the other Bakashos. It is a Bakashah for the entire nation, and not for specifically an individual's request, and therefore it may be recited on Shabbos. Why, though, is it placed in the "Hoda'ah" section of Shemoneh Esreh?
It comes in the section of Hoda'ah because it shows the Jew's ultimate longing to reach Shleimus (from the word "Shalom") in his service of Hash-m. The greatest expression of appreciation that a servant can show to his master is the expression of his desire to serve his master as fully as possible. That is what we are asking in the Berachah of Sim Shalom (based on the explanation of RAV ELIYAHU MUNK, zt'l, in "Olam ha'Tefilos" (Eng. "World of Prayer")).
(P.S. We are sending a copy of your question to the son of Rav E. Munk zt'l, who might have some additional comments to share with us.)
The Gemara clearly gives the reason that Shalom follows Avodah and Hodo'oh and brings the Pasuk, "v'Samu Es Shemi... v'Ani Avorachem" and says that "Hashem's blessing is Shalom." So it is obvious why the last Berachah is Shalom.
The question, however, is why is it phrased in the Lashon of Bakashah -- "*Sim Shalom*... *Barcheinu* Avinu...," and so, too, "Shalom Rav Al Yisrael Amcha *Tasim*"? The same question, however, also applies to Retzei, which is also phrased in the Lashon of Bakashah.
This question is addressed by the Rishonim. The TUR (OC 112) cites the BEHAG, RABEINU TAM, and RI: "It is only individual needs that one may not ask [in the first or third section of Shemoneh Esrei], but needs of the Tzibur are permitted to ask for, as all of the last Berachos are needs of the Tzibur. When the servant expresses the praise of the master, he may ask for the needs of the Tzibur, because this itself is a great praise and honor to the Master -- that everyone relies on Him."
This is also what the RASHBA writes (Berachos 34b, as cited by the BEIS YOSEF): "The blessing of Sim Shalom is also a need of all the people [and therefore it is permitted to ask for it in the last section of Shemoneh Esrei]."
The Shemoneh Esreh was designed to end with "Hamevorech Es Amo Yisroel Basholom", just like Birkas Kohanim ends with "Veyosem Lecho Sholom" and Kadish ends with Shalom, because the ultimate goal is Shalom (or "Shleimus", to use my father's comment) and unity in the heavens and on earth.