Two sisters who disappeared from Rhode Island with their mother in 1985 have been located in the Houston area, and their mother was charged with snatching them, police announced Tuesday.

An anonymous tip two days before Christmas led police to Kimberly and Kelly Yates and their 69-year-old mother, Elaine, said Rhode Island State Police Lt. Col. Joseph Philbin. Elaine Yates, who had been living in Houston under the name Leina Waldberg, was arrested Monday without incident and faces arraignment Wednesday in Rhode Island on a fugitive charge.

Kelly was 10 months old and her sister was 3 when they disappeared. Kelly, 32, and Kimberly, 35, were not living with their mother but are in the Houston area and are in good health, Philbin said.

The girls’ father, Russell Yates, told the Providence Journal in a 1988 magazine story that his wife had discovered he had been unfaithful to her and had threatened to move out in the middle of the night with the children. He came home about 2 a.m. after work on Aug. 27, 1985, and found them gone.

The case was featured on “America’s Most Wanted,” and police received tips from all over the country, including from Colorado and Florida. Investigators reviewed the case and spoke with Russell Yates at least once a year, Philbin said. But it wasn’t until they received the anonymous…