Combatfitness.com Muay Thai Trainer Nicholas Carter (Nico) demonstrates Upper Cut Elbow.
Of all Muay Thai elbows this is the most simple. Just as if you were combing the hair slide hand back over top of the head allowing the elbow to strike upward. Repeat left / right side. In addition to throwing this technique you can also step towards the opponent which can help increase effectiveness/damage. This technique is great for offense and can even be used as defense to block an attack such as hook punch or by allowing an attacker/opponent to run into the elbow if advancing on you.
Remember, chin down and hands in high guard.