The conus elasticus is the lateral portion of the cricothyroid ligament

Cricothyroid ligament

The cricothyroid ligament is the larger part of the laryngeal membrane, continuing inferiorly as a median or anterior part and twin lateral ligaments....

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The lateral portions are thinner and lie close under the mucous membrane of the larynx

Larynx

The larynx , commonly called the voice box, is an organ in the neck of amphibians, reptiles and mammals involved in breathing, sound production, and protecting the trachea against food aspiration. It manipulates pitch and volume...

; they extend from the superior border of the cricoid cartilage to the inferior margin of the vocal ligaments, with which they are continuous.

These ligaments may therefore be regarded as the free borders of the lateral portions of the conus elasticus, and extend from the vocal processes of the arytenoid cartilage

Arytenoid cartilage

The arytenoid cartilages are a pair of small three-sided pyramids which form part of the larynx, to which the vocal folds are attached...

s to the angle of the thyroid cartilage

Thyroid cartilage

The thyroid cartilage is the largest of the nine cartilages that make up the laryngeal skeleton, the cartilage structure in and around the trachea that contains the larynx....

about midway between its upper and lower borders.