The board of directors of Riggs National Corp., holding company for the Riggs National Bank, proposed yesterday a vast expansion in the number of shares in the corporation in an another apparent step to get ready for changes coming in the financial industry.

The banking company also reported that earnings for the third quarter both before and after securities transactions declined by 5.9 percent from $6.817 million ($2.14 a share) in the 1980 period to $6.414 million ($2.29) in 1981.

The board voted to recommend to shareholders that the number of authorized shares of its common stock be tripled from 5 million to 15 million, and that 5 million shares of a new preferred stock be created.

The board had previously approved a proposal to split each share of common stock into two shares, an option that will be considered with the others by shareholders at a special stockholders meeting Nov. 20.

The effect of the actions is to lower the price of the bank company's stock and then make more of it available for purchase. That action, the bank said, is aimed at providing more flexibility for Riggs for such purposes as possible acquisitions and responding to changes in the banking industry.

With such changes as interstate banking and removing barriers that separate banks from savings and loan associations possibly in the offing, Riggs and other Washington area banks have begun making structural changes to move swiftly in the heightened competition when the rules are revised.

Setting up a bank holding company was one such change. Riggs is also said to be discussing some type of joint kiosk venture with Maryland and Virginia banks in which customers of three banks might be able to use a bank machine in any of the three jurisdictions.

The increase in the number of authorized shares of common stock would reduce the par value $5 to $2.50 per share, the same value accomplished by the split. The 5 million shares of preferred would have a par value of $1.

In addition to the third-quarter earnings, Riggs reported a decline in profits for the nine months ended Sept. 30 to $18.49 million ($6.18) from $19.354 million ($6.47) for the same period a year ago.