A locking fastener assembly comprising a nut and a washer. The nut and washer each have opposed load bearing surfaces which include a series of annularly extending, slightly inclined faces forming shallow undulations around each surface. The load bearing surface on the nut is generally spherically convex and the load bearing surface on the washer is generally spherically concave. The nut rotates as it is installed while the washer is prevented from rotating so that the undulating bearing surface on the nut slides over the undulating bearing surface on the washer against ever increasing resistance until the assembly is properly seated and the nut is effectively prevented from counter-rotating by interference between opposed, inclined faces. A concave clamping surface is formed on the outer end of the washer on a radially extending flange. The flange flexes when the assembly is installed and resiliently urges the washer against the nut.