Abstract: An angular and radial self-aligning coupling includes a first support block having a flow bore therethrough with an enlarged counterbore around one outlet of the flow bore. The enlarged counterbore forms a convex annular surface. A spherical seal plate also having a flow bore therethrough includes a concave surface on one side which matingly engages the convex annular surface of the support block. The spherical seal plate also has an annular bearing surface on its other side which engages a bearing face on a radial seal plate. The radial seal plate includes a stab counterbore on its other side. A second support block includes a flow bore therethrough and includes a piston which may be hydraulically actuated to an extended position. Upon actuation of the piston, the piston enters the stab counterbore and the radial seal plate and spherical seal plate automatically adjust for any radial or angular misalignment to allow the piston to stab within the stab counterbore.