The Bracha Rishona on Vegetable Soup is Borei Pri Hoadama, and the Bracha Acharona is Borei Nefashos.
The Bracha is Hoadama if there are large pieces of vegetables in the soup. However if the soup is pureed, since the vegetables are no longer noticeable, it loses it's Hoadama status and becomes Shehakol. (Ben Ish Chai Pinchos 3, Vzos Habracha 12-4, Sharei Habracha 17-46)
Blessed are You Hashem our God King of the universe, Who creates the fruits of the ground.
Baruch Atah Adonai, Eloheinu Melech Haolam, Borei Pri Hoadama.
Blessed are You, Hashem our God, King of the universe, Who creates numerous living things with their deficiencies; for all that You have created with which to maintain the life of every being. Blessed is He, the life of the worlds.
Baruch Atah Adonai Eloheinu Melech Haolam, Borei Nefashos Rabos V'chesronan Al Kol Ma Shebarasa L'hachayos Bahem Nefesh Kol Chai, Baruch Chei Haolamim.
ר' פנחס אליהו בן יעקב יוסף זצ"ל
ר' חיים יצחק בן דוד זצ"ל
In Memory Of