One of the classic rays of saving money is to eliminate the middleman. That can even be done in Wall Street, where hundreds of major companies now sell shares directly to the public, cutting out both the stockholder and his comission.

At least 43 percent of these companies offer new shares at 5 percent below the market price. In short, for every 19 share you buy, you get one free. Some investors use the bargain price to increase their holding of the company's shares. Others buy at the discount and resell immediately, pocketing a guaranteed 5 percent profit.

The basic plan from which all these savings spring is the dividend reinvestment plan, at present offered by more than 9000 corporations, according to a recent study by Salomon Brothers. Instead of receiving your dividends in cash each quarter, you can arrange to have them reinvested in the company's stock.

Most companies absorb the full cost of brokerage commissions when dividends are reinvested. (A few, however, charge part of the commission to you, in which case the plan is less attractive.)

Generally speaking, in any given quarter you have to reinvest all your dividends or none. But some companies will accept partial reinvestment.

In most of these plans, your only saving is the brokerage commission. But three years ago, American Telephone and Telegraph startled the financial community by announcing that its dividend could now be used to buy new shares at 5 percent below the market price.

AT&T has a larger number of shareholders than any other corporation in America. Its discount policy helped in raise $473 million in new capital in 1977 alone-a lessen that was not lost on other corporations hungry for funds. Since the big utility's grand climbed on the bandwagon, and many more will certainly follow.

You'll find a list of most of the companies with discount policy in the October issue of 'Dun's Review" (look for it in your library). Many are utilities, a popular and high-yielding investment. The group also includes some industrial and financial corporations such as Allied Chemical, Crocker National, International Paper, Kemper, Standard Brands and Union Carbide.

All the companies on Dun's list, as well as many others, make yet another money-saving offer to shareholders. Every quarter, you can buy a certain number of shares from the company for cash. There's generally no five percent discount, but you save most or all the brokerage fees.

The purchase of just one share of stock through a stockbroker (or five or ten shares, depending on your broker's minimum) opens the door to all the benefits of direct sale. With that one share in hand, you can subsequently invest $3,000, $5,000 or even $15,000 each quarter (depending on the company's limits) at no additional cost.

On a $3,000 investment in AT&T, your saving in brokerage commissions would run in the area of $45. On a $5,000 investment, in Union Carbide, uou'd save perhaps $93.

If you take advantage of all these bargain offers, what's your tax picture? Dividends are taxable in the year in which you receive them, even if they're reinvested in company stock. But you have a $100 exclusion, if he or she also wons stock or owns stock jointly with you.

If you receive the stock at less than market price, the difference between your bargain price and market price when the stock was acquired is also considered current income, and taxed. In other words, if you paid $4,750 for stock worth $5,000, the $250 of instant profit is taxed as income.

As you might imagine, a good many stockbrokers are not happy with dividend reinvestment and cash-purchase plans that cut them out of commission business. For this reason, they may not call your attention to the plans, or to the corporations that offer them.

If you happen to own shares in such a company, information on these money-saving benefits will be contained in the literature the company sends you. So don't neglect to open those envelopes, and read the material. Even if your company isn't now offering dividend reinvestment or cash-purchase, it may in the future.