National Steel Corp., the nation's third largest steel manufacturer, agreed to buy one of the nation's largest savings and loan businesses yesterday in what was described as a radical departure for both industries.

Pittsburgh-based National announced an agreement in priciple to buy United Financial Corp. of California, owner of the 12th largest savings institution in the country, for $243.6 million.

The steel company's takeover bid, approved by United Chairman Anthony Frank, sent the generally depressed prices of publicly traded savings and loan institutions' stock sharply higher. In a wave of buying, United shares jumped 53 percent on the New York Stock Exchange to $36.25, up $12.625 for the day.

National Steel offered to pay $42 a share for each of the 5.8 million shares of United Financial outstanding in what would be the largest S&L takeover transaction on record.

United Financial owns Citizens Savings and Loan, based in San Francisco, with assets fo $2.6 billion. Founded in 1885, Citizens S&L has more than 75 offices throughout the greater San Francisco and Los Angeles regions. United itself is the sixth largest publicly owned S&L company in the nation.

Officers of National Steel, like many other firms in the industry, have been concerned in recent years about the cyclical nature of the steel business, which ranges from boom to bust years.

Therefore, National's move yesterday to diversify was not surprising. But the move into financial services instead of other manufacturing shocked Wall Street.

"I am appalled at George Stinson [chairman of National Steel]. It is a real radical move... a step out of character," said one analyst.

But Stinson said the proposed takeover "is an important step in the diversification that National Steel has sought for some time."

He said the steel industry's problems -- enormous consumption of money, large labor forces, and vulnerability to imports and extensive environmental controls -- "do not, in the main, exist in the fields of financial services."

For these reasons, "United Financial will make a significant contribution to broadening our base and stabilizing our profitability," Stinson added.

Last year, National shipped 8.2 million tons of steel -- about 8 1/2 percent of the industry total. For 1973 through 1977, some 95 percent or more of National sales came from steel products, with the balance from aluminum -- reflecting a narrowly construed metals company.

Although a steel manufacturer's entry into the savings and loan business came as a surprise yesterday, a bid by some company for a large California S&L had been expected. Eleven of the nation's 15 largest S&Ls are in California, where state regulation has fostered fierce competition.

In the last 18 months, about a dozen smaller S&Ls in California and Texas have been acquired by consumer finance, real estate, insurance or other S&L interests, as well as individuals, according to Jerry Gitt of the San Francisco office of Dean Witter Reynolds.

"I'm surprised by who the buyer is but I'm not surprised by the offer" nor by the National bid being $21 a share higher than United Financial stock was being sold for last week, Gitt added. Most S&L stocks have been trading at less than 80 percent of listed value, and Gitt said that the S&Ls which have been sold were purchased at up to twice the book value.

Although S&L industry analysts said yesterday they expect no difficulty in gaining regulatory agency approval for the National Steel acquisithe proposal is certain to attract some critical attention on Capitol Hill because S&Ls traditionally have been local businesses organized to provide home mortgages from a poor of consumer savings.

One congressional aide yesterday said there may be questions about interlocking boards of directors and loan policies if a trend continues of S&Ls being taken over by non-financial companies in addition, the industry which National Steel has picked for diversification is itself cyclical -- with profitability tied to interest rates.

Last year, with interest rates soaring, United's profits jumped 21 percent to $28.5 million ($4.86 a share) and, for the last nine years, earnings were up tenfold. National profits in 1978 were $112.4 million on sales of $3.8 billion. Generally, National is regared as one of the better-managed firms in the depressed steel industry.

No other steel firm is engaged in S&L operations, although Armco Steel has a lending subsidiary, Armco Industrial Credit Corp., which makes loans to industrial companies. The credit operation has a loan portfolio of $150 million and is being expanded as part of Armco's own diversification.

On balance, analysts said National's bold move represented a radical, if not risky, Venture. "I'm going to call George Stinson tomorrow and find out what the hell he's doing," one analyst stated.

United Financial Chairman Frank said, however, that National's move is "not a watershed" event. In a telephone interview, Frank noted that retail giant Sears, Roebuck owns a large California S&L and that MCA, the entertainment conglomerate, has an S&L in Colorado. A number of smaller S&Ls have been bought recently by industrial firms.

"This was an unsolicited offer, we were not looking to sell... but as we got to the premium they were offering, substantially over the market, we said: 'What's best for the stockholders?'" Frank added.