During routine dissection for First MBBS students on a 65 years donated embalmed male cadaver in the Department of Anatomy, K.J.Somaiya Medical College, we observed an entrapment of brachial artery and median nerve by coracobrachialis and brachialis muscles. The median nerve and the brachial artery passed through the coracobrachialis muscle in the right arm. The superficial fibres of the coracobrachialis muscle were normal in their insertion i.e. on the middle 5 cm of the medial border of the shaft of the humerus. We also encountered an accessory slip of the brachialis muscle originated from anteromedial surface of the shaft of humerus and got inserted into the medial epicondyle of the humerus. The accessory slip of the brachialis muscle passed over the brachial artery and the median nerve. This may result in neurovascular compression and it may have some mechanical advantages and disadvantages during the movement of elbow joint. The knowledge of such variations were important for medical fraternity such as surgeons, orthopaedicians, neurologists, radiologists and physiotherapist for dealing with injuries or operations around the elbow joint.