Hello. When I put my hands under my left ribcage, I can move something made of bone back and forth over the edge of my ribs. Is this normal?

Costal Cartilage. Where the ribs attached to the Cartlidge can be an area that can be injured or broken. I suspect this is what your symptom is. You need to know valuation to help clarify that. If it’s not painful there may not be much you have to do.