Acting on a confidential tip, officers said, a search centered on a tract off of La. 10, between Mamou in Evangeline Parish and Oakdale in Allen Parish.
Shunick has been missing since May 19, last seen as she bicycled toward her home in Lafayette about 2 a.m.
Brandon Scott Lavergne, 33, of Swords, near Church Point, was subsequently charged with her murder and that of a Youngsville woman in 1999. He has pleaded not guilty to both charges.
Lafayette Police Department Information Officer Paul Mouton said police believe they have located Shunick, though a positive identification had not been made as darkness fell over the rural site.
Mouton could not comment on where the tip on Shunick's possible resting place came from, particulary whether Lavergne led them to the site.
Lafayette Police Chief Jim Craft said official word on the identification of the remains recovered Tuesday will come through the proper officials after laboratory tests are conducted.