A locking system 10 for mechanically joining a plurality of panels 16, 18 or components 12, 14 of an article of construction without the need for glue or other adhesive is provided Each panel 16, 18 includes first and second locking members 26,28 spaced beneath its outer surface 20 The first locking member 26 is at one side edge 22 of the panel and has two spaced-apart flexible arm portions 34, 36 at least one arm portion including a first latching member 54. The second locking member 28 is at another side edge 24 and includes a channel 70 recessed within the side edge. The channel 70 is sized to receive the arm portions 34, 36 without them having to contact th channel 70 unless deflected within the channel 70. The second latching member 56 is preferably a slot 72,74 abutting the channel 70.