Given a sequence of numbers which can be mapped into an m multiplied by n array, sorting rows and columns is shown to yield an overall sorted sequence. This unusually simple procedure is shown to require O(log//2 m) iterations by analyzing the data movement in the array under successive row and column sorts. An efficient bubble sort network suitable for VLSI implementation, with near-optimal area-time**2 performance, is a direct application of the row-column sorting technique. The ease of implementation for practical VLSI chips is also demonstrated.