A new cultivar of Azalea named ‘AZ 35’ that is characterized by its compact, rounded plant habit with a top to bottom leaf canopy, its two distinct blooming periods from late March to early April and from late July into September in Texas and Mississippi, its spider form petals, that are pink in color and elongated in the spring and less elongated and tinted lavender in the fall, its narrow, sandpaper-textured foliage that is light green in color and blushed purple in the winter, its high level of resistance to spider mites, aphids, lace bugs, its high tolerance to heat stress, its stem and flower buds that are resistant to cold damage down to 14° F., its ease and speed of propagation by cuttings, and its very vigorous growth rate.