Yep, that’s what an elevator is, an elevator is essentially a Faraday cage (A metal box, No RF signals in or out) Also, it’s located inside another steel-reinforced concrete space – the elevator shaft which in turn is located inside the multiple story building we mentioned above.
Because of that the cell signal typically can’t reach your phone when you’re in an elevator and the truth is, even if the tower signal could get to your phone inside the elevator, it would be virtually impossible for the transmitter on your phone to send its signal back to the cell tower to complete the communications loop. There are just too many layers of concrete and steel for your signal to pass-through.
The only reliable way to get a cellular signal to a phone inside an elevator is to have in place a cell signal boosting system.
There are different versions of these devices, so it is essential to pick the one that is the most appropriate in each case. The best way to do that is by taking readings in and around the building with a machine called a scanner and analyze the results.