Activist investor Starboard Value reported a 5.6 percent stake in MeadWestvaco and said the packaging materials maker's stock was "deeply undervalued."
MeadWestvaco's shares rose as much as 5 percent after Starboard, in a letter to the company, also said its management should take steps to improve operating margins and capital allocation and consider separating non-core assets. (Click here to track MeadWestvaco's shares.)
The company has the highest ratio of selling, general and administrative expenses to sales in the industry due to excessive corporate expenses and higher-than-average operating costs, Starboard said in the letter, released on Monday.
About 12 percent of the company's revenue went into selling, general and administrative expenses in 2013 compared with about 9 percent for rivals Packaging Corp of America and Graphic Packaging Holding Co.
MeadWestvaco, which makes packaging materials for the healthcare, personal care, food and beverage, and agricultural industries, has a market value of about $7 billion.
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.
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.