The reason for dark elbows or knees could be due to pigmentation of the skin and scrubbing with soap alone would not help.
Here are some simple remedies to lighten the skin tone of your elbows and knees.
Aloe Vera
It is a great way to make your skin supple. All you need is a aloe vera leaf. You need to break open one of the leaves of aloe vera and apply the pulp on your elbows and knees. After 20 minutes rinse with cold water.