Diaper Packaging Garbage or Special Recycling Drop-Off Soft plastics, known as film plastics, should be placed in your garbage can, or can be brought to a film plastic recycling drop-off location. Find your closest drop-off location. Must Be Dry and Clean If diaper packaging is wet or dirty, it cannot be recycled because it would contaminate the plastic recycling. Make sure to put it in the trash. Ways to Reduce Switch to Cloth Diapers Consider switching to cloth diapers, which are more eco-friendly than disposable ones because you can wash and reuse them.