Wall Street securities analyst Elliot Schneider has started an election campaign to become a director of the embattled Federal National Mortgage Association.

Schneider, a long-time stockholder of the Washington firm, earlier charged that the Department of Housing and Urban Development is playing a "game of chicken" in attempts to gain more of a say in FNMA operations

But the analyst, who works for Gruntal & Co. in New York, also has criticized the methods adopted by corporate leadership at FNMA in seeking to counter attacks by HUD.

Undeer the leadership of Secretary Patricial Roberts Harris, HUD has sought to change the management of the company, called Fannie Mae. In addition, HUD had proposed a significant increase in its regulatory oversight of the company's mortage purchases an effort to increase urban leanding.

In a letter being distributed today, Schneider says a number of Fannie Mae stockholders have expressed "dissatisfaction to me with the way FNMA's board of directors has chosen to defend the company's integrity from Secretary Harris' unrelenting attacks."

In effect, Schneider adds, "I've been challenged to put my body where my mouth and money are by running for the broad of directors . . ."

The analyst said te possibility of his election is not "so far-fetched," because FNMA has cumulative voting -- permitting each owner to cast all shares for just one candidate.

Schneider says he is not becoming a candidate because he thinks current stockholder-elected directors are wrong in opposing Harris or because of any "significant difference with the operating management of the compay."

Rather, he says, "FNMA will be helped by the presence on the board of someone whose sole interest, so far as the company's business is concerned, is the long-term interest of the common shareholders."