Exercises With Hand Weights to Strengthen the Neck & Shoulder Muscles. Part of the series: LS - Workouts for a Better Body. If you sit for long periods of time working at a desk, then you’re going to want to do dumbbell shoulder shrugs to alleviate the tension in your neck and shoulders. Find out about exercises with hand weights to strengthen the neck and shoulder muscles with help from a graduate of the United States Military Academy at West Point in this free video clip.