The present invention is a polyaxial locking screw plate assembly for immobilization of vertebral bones, via fixation to surfaces thereof. The assembly includes a plate, having an upper portion and a lower portion, each of which has a pair of tapered holes, into which holes coupling elements and bone screws may be inserted. The upper part of the holes further includes an annularly recessed channel in which a snap-ring is disposed. The coupling elements each have an axial taper which matches the taper of the holes, and an interior semi-spherical concave surface in which the semi-spherical head of a bone screw may be polyaxially mounted. The bone screws are inserted through the holes until the coupling element engages and expands the snap-ring. Once the coupling element is fully seated in the hole, thereby locking the screw in place and the coupling element in the hole, the snap-ring contracts to its undeflected position and prevents the coupling element and screw from backing out of the hole in the event of loosening.