I also encourage students to read by rewarding them with points/stickers. I have done it with kindergarten students right up through college students.
once a reward is attached to volunteering to read, you'll get most of your students stepping up. i reward my young students with stickers and stamps and my older students with participation points.
literally, i can get almost everyone in the class to volunteer when i reward them. sometimes so many people volunteer that the material runs out and there's nothing left to read.