Shell Oil Co. said yesterday that the past winter's harsh weather and higher exploration costs drove profits down 18.4 per cent in the first quarter.

Shell's announcement follows Exxon Corp's report Monday that profits dipped 11.6 per cent in the quarter.

Shell said it earned $169 million in the first quarter, compared with $202 million in the first quarter of 1976. Per-share earnings feel from $2.93 to $2.39, but sales rose from $2.3 billion to $2.5 billion.

"Significant events affecting earnings in the quarter were higher operating expenses caused by abnormally cold weather, inflation, increased dry hole costs associated with greater exploration activity and the recent increases in foreign crude oil prices." Shell President John F. Bookout said.

"Chemical products sales volumes were lower in January and February than expected because of severe winter storms which caused plant shutdowns for many of Shell's chemical customers," Bookout said.

AMong other oil companies, Sun Co. said its quarterly earnings declined to $81.5 million, or $1.38 a share, from $86.5 million or $1.43 a share, a year ago. Sales rose from $1.2 billion to $1.6 billion.

Texaco Inc. said it earned $242.6 million, or 89 cents a share, on revenue of $7.1 billion in the first quarter. A year ago, Texaco earned $223.7 million, or 82 cents a share, on revenue of $5.3 billion.

Phillips Petroleum Co. said earnings rose from $97.5 million, or $1.28 a share, a year ago to $122 million, or $1.59 a share largely on income from North Sea oil production. Revenue rose from $1.4 billion to $1.6 billion.

Cities Service Co. reported a 21 per cent increase today in net income for the first quarter of the year compared with the same period in 1976.

Gerry Oil Co. earned $4.10 a share in the first quarter, up from $3.08 a year ago.