The trachealis muscle is a smooth muscle that bridges the gap between the free ends of C-shaped cartilages at the posterior border of the trachea, adjacent to the esophagus.The primary function of the trachealis muscle is to constrict the trachea, allowing air to be expelled with more force e.g. during coughing.he trachealis muscle is a smooth muscle that bridges the gap between the free ends of C-shaped cartilages at the posterior border of the trachea, adjacent to the esophagus. The primary function of the trachealis muscle is to constrict the trachea, allowing air to be expelled with more force e.g. during coughing.