NEW YORK – With its annual meeting looming and its stock on the decline, Apple Inc. is facing a rebellion from an influential investor who wants the company to stop stockpiling cash and give it to shareholders instead.

Greenlight Capital said Thursday that it is suing Apple in a New York federal court over the company’s proposal to make it more difficult for it to issue preferred stock. David Einhorn, who heads the investment fund, said the proposal would close down one avenue for Apple to reward shareholders with more cash.

Apple is still the world’s most valuable company, but its stock has lost 35 percent of its value since September as its once-rapid growth has slowed. The company is fabulously profitable, and Wall Street wants the company to share more of that money with its shareholders rather than tucking it away in low-yielding bank accounts.

“Apple has $145 per share of cash on its balance sheet. As a shareholder, this is your money,” Einhorn said in a letter to the company. He has a history of criticizing companies publicly, often after shorting their stocks.

In a statement Thursday, Apple said its management and board continue “active discussions” about what to do with the money, and it will take Einhorn’s proposal into consideration.

Its $137 billion in cash makes up nearly a third of Apple’s stock market value. Shares of the Cupertino, Calif., company closed at $468.22 Thursday, up 3 percent for the day.

Corporations normally don’t hoard cash the way Apple does. They keep enough on hand for immediate needs, and either invest the rest in their operations or hand it out to shareholders in the form of dividends or stock buybacks. If they need more cash for, say, an acquisition, they borrow it.

Einhorn told CNBC on Thursday that Apple was acting like his grandmother “Roz,” who grew up during the Great Depression. People who have experienced financial trauma, he said, “sometimes feel like they can never have enough cash.”

Einhorn’s criticism hints at Apple’s lean years in the mid-90s. Former CEO Steve Jobs came out of that experience with a very tight hold on the company’s purse strings. Apple has never explained its reasons for hoarding the cash other than to say it is preserving its options. Since his death in October 2011, Apple has begun paying a quarterly dividend of $2.65 per share and started to repurchase some of its shares.

Analysts say the company should be doing more if it wants to lure investors back to its shares. Stuart Jeffrey at Nomura Securities calculates that Apple will generate about another $103 billion over three years to add to the $137 billion it has now, but it has only committed to returning $45 billion of this $240 billion in total cash to shareholders.