Technically, any type of mattress can be fiberglass-free. Certain types of beds are simply more or less likely to contain fiberglass. Organic latex mattresses and natural latex mattresses are most likely to be fiberglass-free and instead contain wool or silica.
Conversely, memory foam and polyfoam mattresses are more likely to contain fiberglass. If these types of mattresses intrigue you, double-check the bed’s specifications to ensure it’s fiberglass-free.