An elevator cable safety brake is disclosed. The brake includes a first housing which is slidably mounted in a second housing. The first housing has an opening through which the elevator cables can pass. On one side of the elevator cables is located a first brake pad which is carried by the first housing. On the other side of the opening is located a second brake pad which is generally wedge shaped. The second brake pad is carried on a sled which is slidably housed within the first housing. The second brake pad may be moved between a free running position and a braking position. The wedge shaped second brake pad may be selectively released under certain trip conditions from the free running position to the braking position. Such conditions include the unintended overspeed operation of the elevator, a power failure, or the elevator commencing movement before the elevator doors are fully closed. A governor trips a trip lever effecting the release of the second wedge shaped brake pad. The slidable interaction between the sled and the first housing and the second housing enables the brake device to be self centering around the cables during the braking action. In an alternate embodiment the safety brake works in both the up and down directions.