Sometime next month, a computer at Giant Food headqarters in Landover will phone a computer at Nabisco's offices in New Jersey and order a truckload of shredded wheat.

The Nabisco computer will authorize the shipment, notify Giant's computer when it's coming and electronically transmit the bill.

When the cereal arrives, Giant's computer will crank out a check -- the first piece of paper in a computer-to-computer ordering system that will be tested this fall by the food industry.

Called the Uniform Communications System, the paperless chain is being put together by the same kind of industry-wide task force that created the Universal Product Code -- the little stripes on food containers that allow computerized checkouts to ring up sales electronically.

"UCS will do for the back room what the UPC did for the front end," predicted Donald R. Buchanan, Giant's vice president for data processing.

Computerizing the checkouts was the first step, he explained, because the payback on the capital investment came quicker.

Now the food industry is preparing to extend the computer control upstream, using the UPC's product-identification numbers for transactions between stores and their suppliers.

Estimates are that the industry will save $300 million to $400 million a year with computer-to-computer ordering.

Behind the project are half a dozen Washington-based trade groups -- Food Marketing Institute, Grocery Manufacturers of America, National Association of Retail Grocers, National American Wholesale Grocers Association, National Food Brokers Association and Co-operative Food Distributors of America.

The 13 companies participating in the first test besides Giant and Nabisco include RMI Inc., an Elkridge, Md., food broker; Safeway Stores Inc.; such manufacturers as Kraft Inc., Dow Chemical Co., Procter & Gamble Co. and Chesebrough-Pond's Inc.

Most of the test project firms worked on industry committees that created a standard format for all food orders, a computerized fill-in-the-blanks form that any retailer will be able to use to order from any manufacturer, wholesaler or broker.

This fall, they will see whether it works.

At first conventional paper orders and invoices will be used in addition to the computer-to-computer link, Buchanan said. "When our people are satisfied, we'll do it all by computer" and drop the parallel paper system.

Next January, Giant, RMI and the other pilot project participants are to report to the industry on their experiences. Then, assuming all goes well, others join up.

"There's no question in my mind that it will be a success," Buchanan said. "Our objective is to get as many manufacturers as possible on the system as quickly as possible."

The industry's estimates of cost-saving are based on the assumption that 50 percent of all orders are handled by computer. Because the food business is dominated by big chains and big brand-name suppliers, that 50 percent goal can be reached by signing up a relatively small share of the companies in the field.

Buchanan says Giant expects "some significant savings, but I won't tell you how much because it's premature."

The savings are expeced to come from minimizing mistakes, eliminating repetition of some steps of the ordering process, doing away with paper and, most importantly, saving the time it takes to mail an order.

Giant officials estimate they can cut at least two days, and in some cases a week, off the lead time on orders with a computer-to-computer link.

If a corn canner takes five days to deliver a new batch to Giant, and it takes two days for the order to get there by mail, then the chain has to reorder seven days before it expects to need more corn.

If the two days' mailing time can be eliminated, the warehouse can get along with two days' less inventory, reducing the cash tied up in warehouse stocks.

Like all the big food chains, Giant's warehouse inventory is already managed by a computer system. It not only keeps track of stocks, but also knows how fast items sell and how fast manufacturers ship, so orders can be timed for precise management of cash and commodities.

With computerized checkouts in every store and a computerized warehouse, is Giant headed for an all-computer control system? Will pulling a can of corn across the computerized checkout someday trigger a series of signals that will automatically order another batch from the maker?

"I don't believe that will ever happen," says Buchanan, who has seen computer checkouts sweep the industry in less than a decade.

Computers can't beat a store manager for eyeballing the aisles to see what's selling, he explained. Computers can't account for the October blizzard that produces a run on groceries, or keep track of the competitor across the street. "There has to be human intervention."