Final answer:
The rigid layer surrounding plant cells is called the cell wall, comprising mainly of cellulose and providing structure and protection.
Step-by-step explanation:
The rigid layer of non-living material that surrounds the cells of plants and some other organisms is called the cell wall. The cell wall is an external structure to the plasma membrane and is essential for providing protection, maintaining structure, and determining the shape of the cell. In the context of plant cells, the cell wall is primarily comprised of cellulose, which is a polysaccharide formed of glucose units. An example of the cell wall's rigidity can be observed when biting into a raw vegetable, such as celery, which crunches due to the tearing of its cell walls.