Combine butter and cream cheese in a medium mixing bowl. Gradually add sugar, beating until light and fluffy. Stir in flour and apricots. Mix well.
Shape into a roll, 1-inch in diameter. Wrap in waxed paper, and chill 3 hours or until firm.
Cut into 1/4-inch slices; place 1 inch apart on ungreased cookie sheets. Bake at 350° for 8 to 10 minutes. Remove from cookie sheets, and cool on wire racks.