Shug Share definition Flag Found in border towns, and Mexican beach towns. Shug means to get a Shower and a Tug. I didn't sleep with any hookers in Mexico, I just got a shug. For his 18th birthday I bought him a shug. Shug by Marcass1 March 21, 2009 0 0 Get merch Get the Shug mug. Buy Now — $32.95 See more merch