The fibers of a mattress are like any other fabric; smells and scents can permeate the fabric and remain buried deep inside the fibers. For those who smoke, ridding your home of cigarette smoke can be difficult. Fortunately, removing smoke odor from a mattress is easy. Remove the mattress from the box spring and place it on the floor. Take ordinary banking soda and sprinkle it on the mattress. It is important to liberally cover the mattress in a layer of powder. Don't worry about using too much. Allow the mattress to sit overnight if possible. If this is the only available mattress in the house, allow it to sit for as long as you can. The baking soda needs time to draw the odors out of the mattress so the longer the better. Use a vacuum cleaner to remove the baking soda from the mattress. Be very careful to remove all of the baking soda. Turn the mattress over and repeat on the other side. If the mattress was exposed to very heavy smoke such as a house fire, repeat as necessary.