International Paper Co. earned $10.96 a share last year, up from $4.94 in 1978.

Much of the profit, however, was gain on the sale of the general crude oil petroleum properties, a paper mill at Panama City, Fla., and Woodlands, N.Y.

There were other extraordinary items that affected the earnings for both years. Without these, the company said the earnings for 1979 would have been $276 million ($5.73 a share) up from $251 million ($5.30) in 1978.

Aluminum Company of America reported fourth-quarter 1979 net income of $135.1 million ($3.82) compared with fourth quarter 1978 net income of $100.3 million ($2.85).

Alcoa said net income for all of 1979 totaled $504.6 million, against $312.7 million in 1978.

It said sales and operating revenues in 1979 were $4.8 billion compared to $4.1 billion in 1978, and shipments of aluminum products were 1.886 million tons, compared with 1.779 million tons in 1978.

Republic Steel Corp., the nation's fifth largest steel maker, reported a sharp decline in fourth-quarter earnings and predicted yesterday that 1980 steel shipments would drop by 10 percent.

But Republic Chairman W. J. DeLancey, said, "Beyond the current recession, we see steady growth for the steel industry in the 1980s."