The company could not be immediately reached for comment.
MeadWestvaco said in January that it would cut costs and target savings of $100 million to $125 million by the end of 2015.
The company could slash costs further by "consolidating regional headquarters, reducing duplicative administrative staff, and flattening the organization structure," Starboard said.
MeadWestvaco should also consider selling or spinning off its specialty chemicals business, the hedge fund said.
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The business, which makes chemicals derived from sawdust and other byproducts of the papermaking process, accounts for about a fifth of the company's total revenue.
MeadWestvaco's shares have gained about 24 percent in the past year, compared with a 21 percent rise in the Dow Jones U.S. Containers and Packaging index.
The stock, which trades at 20.9 times the company's 12-month forward estimated earnings, is expensive compared with shares of International Paper, Packaging Corp, Graphic Packaging and Clearwater Paper Corp, which trade at an average 14.3 times, according to Thomson Reuters StarMine data.
—CNBC.com contributed reporting.