According to Sportsinjuryclinic.net, several muscles in the elbow joint are directly involved in the flexion and extension of the elbow. Two of the largest are the biceps brachii and the triceps brachii.
According to IDEA Health & Fitness Organization, the brachioradialis, the biceps brachii, the brachialis and the anconeus are the main elbow joint muscles involved in flexion. The brachioradialis muscle also assists with extension, even though its primary purpose is flexion. The brachialis is the strongest muscle used in flexion.
As listed by Sportsinjuryclinic.net, some other commonly used muscles in the area of the elbow include the extensor carpi radialis brevis and the pronator teres.