**Core Concept**
The classical radical dissection of the neck, also known as the Crile procedure, is a surgical technique used to remove **cancerous lymph nodes** and other structures in the neck. This procedure involves the removal of various tissues, including **lymph nodes**, **muscles**, and **nerves**, to treat **head and neck cancers**. The goal is to eliminate the cancer while preserving essential functions.

**Why the Correct Answer is Right**
In the Crile procedure, the **sternocleidomastoid muscle** is typically spared, as removing it can lead to significant **shoulder dysfunction** and **cosmetic deformity**. The procedure aims to balance oncological efficacy with functional preservation, making the retention of this muscle a crucial aspect of the surgery. The **accessory nerve**, **internal jugular vein**, and **omohyoid muscle** are often removed or partially resected during this procedure.

**Why Each Wrong Option is Incorrect**
**Option A:** Removing the **accessory nerve** is common in radical neck dissection, as it facilitates the removal of lymph nodes.
**Option B:** The **internal jugular vein** is often removed to ensure thorough clearance of cancerous tissue.
**Option C:** The **omohyoid muscle** may be resected to access deeper lymph node groups.

**Clinical Pearl / High-Yield Fact**
A key point to remember is that the Crile procedure is a comprehensive surgical approach aiming to remove all potentially cancerous tissue while preserving essential structures like the **sternocleidomastoid muscle** for functional and cosmetic reasons.

**Correct Answer:** D. Sternocleidomastoid muscle