Both sides? You mean like the left and right lane? If so, that's exactly what NOT to do. In the USA we "move to the right for sirens and lights" or move over at least 1 lane over if stopped. If you cannot move over, slow down to 10 less than the speed limit.

If everyone moves to the right, that makes space for the emergency vehicle to pass on the left or drive in the on coming lane if needed. This is how we are trained.

Source: 15+ years of people not moving over for me.