Texas State Highway 338State Highway 338 is a state highway in the U.S. state of Texas. The highway begins at a junction with U.S. Highway 259 in Rocky Branch and heads north to a junction with State Highway 77 in Naples.HistorySH 338 was designated on November 22, 1940, to serve as a route between Rocky Branch and Naples.Route descriptionSH 338 begins at a junction with US 259 in Rocky Branch. It heads north from this junction to an intersection with FM 161. SH 338 reaches its northern terminus at SH 77 in Naples.