Trees and shrubs will not affect the system. However, placing the transmitter inside a metal building can reduce the maximum range of the wireless system.
Parking a vehicle within the pet area, can reduce the range of the system and cause your pet to receive a static correction where it otherwise would not if the vehicle was not there.
Fixed large metal objects such as metal sheds can affect the signal by reducing the maximum range of the system at the location of the object. As a result, your pet may receive a static correction. If you have a great deal of metal in your yard that you feel my impact your system, you may want to consider an in-ground wired containment system for you and your pet instead.