A new peach variety, Prunus persica, (hereinafter referred to as the MSUP8706 peach variety), which was developed by Amy Iezzoni and Bill Shane in a breeding program at the Southwest Michigan Research and Extension Center in Benton Harbor, Mich., having the following number of unique and desirable features: 1. A fruit with excellent shipping and storage characteristics. 2. A fruit maturing at the same season as the Loring peach (an unpatented selection). 3. A generally round fruit with freestone, yellow flesh, and an attractive red blush.