The present invention is a polyaxial locking screw plate assembly for immobilization of vertebral bones, via fixation to surfaces thereof. In one embodiment the invention includes a plate, having an upper portion and a lower portion, each of which has a pair of threaded holes, into which holes coupling elements may be screwed. The coupling elements each have a threaded cylindrical exterior, and have an interior semi-spherical concave surface in which the semi-spherical head of a bone screw may be polyaxially mounted. In a second embodiment, the present invention includes a similar plate, having holes which are, however, threaded part of the way through the plate. In this embodiment, the bottom portion of the holes of the plate, additionally, have a curved interior surface which forms an annular lip for supporting a semi-spherical head portion of a bone screw. The coupling element of this embodiment is a short threaded cylindrical piece, having a concave bottom which locks the screw into the hole. Variations of each embodiment have means associated with the holes and/or the coupling element for locking the angle of the screw to the plate. A further variation of the plate of this invention includes a pair of spikes which may be used to temporarily lock the plate to the exposed bone.