Why can I listen to my mobile phone's radio clearly inside the bus, inside the train, but not inside the elevator? Also, there is an interference of radio signal when the train is accelerating or decelerating. What is the reason behind this?
Buses and trains have lots of glass windows, and radio waves will get through glass. An elevator is effectively a metal box and radio waves can't get through metal.
Have a look at the Wikipedia article on Faraday cages. Any metal enclosure, like an elevator, forms a Faraday cage. The wavelength used by mobile phones is 17cm or 33cm depending on the band, so any window of this size or larger will allow the signal through, but windows significantly smaller than this will block the signal.