Apple Computer Inc. shares climbed nearly 2% to new high Tuesday as investors got behind the company’s stock following some recent analyst speculation about iPod sales in the holiday season, along with the belief that Apple is close to getting into the mobile-phone market.

Apple stock recently rose 1.8%, or $1.56, to $88.03 after earlier rising to a high of $88.40, surpassing the previous 52-week high of $87 reached Monday.

While the Cupertino, Calif.-based company is typically tightlipped about its next round of products, some analysts believe that Apple will soon unveil the “iPhone,” which will be Apple’s first name-branded mobile phone. The iPhone is said to include the iTunes music-playing technology and instant-messaging capabilities.

Shaw Wu of American Technology Research wrote in a note that any iPhone remains in the development phase, and it’s not possible to gauge when Apple might release such a device, or with whom the company is partnering with to make the iPhone a reality.

Mr. Wu also said that he expects Apple to sell 14 million iPods in its current fiscal quarter. Such results would be in line with its sales figures in the same period a year ago.

Apple typically uses company events to announce new product releases, and will likely use the annual San Francisco MacWorld Expo in January to debut its next devices.