When running uphill, it is essential to push off the ball of the foot. This movement ensures a lighter touch off the ground and, along with regular breathing, optimises energy.
Running downhill requires concentration. It is important to run downhill by pushing the feet as far back as possible, so they are almost brushing the glutes. It is important when running downhill never to push off the heels as this increases exertion and can lead to a loss of balance.
To maintain stability, it is important to wear good shoes. They must offer protection but also be light enough to allow you to run to the best of your ability; in other words, a compromise is needed between a good running shoe and a trekking shoe. It is important that they are able to provide spring and aid momentum while running uphill but also to ensure a sense of safety when running downhill. The sole must provide good grip on rocky terrain (particularly when wet) as well as on snow and ice. A lightweight shoe is also essential and I would advise the shoes must weigh less than 200grams (7oz).