Chaturanga Dandasana, or Plank pose, can be both physically and psychically challenging for the yoga practitioner as the entire weight of the body is balanced across the hands and the toes. It is important to practice this pose in alignment to avoid overstraining the wrists and elbows. Keeping the elbows over the hands at a ninety degree angle and the arms pulled in tightly to the body is correct. Our tendency is to muscle through this pose by only using the front side of the torso, which causes us to incorrectly splay the elbows out and away from the body. This will strain the elbows within a short period of time. Focus on pulling the shoulder blades in and down the back to activate the full strength of your arms. Also, pull the lower abdominal muscles in and up to support the lower body. In doing so, you are utilizing the power of both the back and the front of the body. It is also helpful to strengthen the biceps and triceps with weight lifting if necessary; never depend on your arms alone. This balance is the beauty of yoga--uniting our whole selves--and utilizing all of our power will make the pose more effortless.
Yoga Journal has a great article if you are interested in researching the topic further: