Mr. and Mrs. Stephen Page Smith, of Alexandria, announce the engagement of their daughter, Elizabeth Randolph, to Phillip Thomas DiStanislao III, of Richmond, son of the Reverend Virginia DiStanislao and Mr. Phillip Thomas DiStanislao Jr., of Petersburg.

Miss Smith is a graduate of St. Stephen's and St. Agnes School, Alexandria, and Mary Washington College. She is the granddaughter of Mrs. Edmund Randolph Harrison of Cartersville, the late Mr. Harrison, and the late Mr. and Mrs. Elmer Morgan Smith, of Bowl-ing Green, Kentucky.

Mr. DiStanislao is a graduate of St. Christopher's School and Wake Forest University. He is the grandson of the Honorable and Mrs. Ernest Pleasants Gates, of Chesterfield, Mrs. Marian White DiStanislao, of Petersburg, and the late Dr. Phillip Thomas DiStani-slao, formerly of Petersburg.

An August wedding is planned.