Apple is staying on message about the imminence of the post-PC era proclaimed by CEO Steve Jobs.

In a midweek meeting with Goldman Sachs analyst Bill Shope at Apple headquarters, Chief Operating Officer Tim Cook said he "remained remarkably optimistic about the demand for the iPad and the long-term market opportunity for tablets."

Apple

As a result, Apple's COO sees "no reason why the tablet market shouldn't eclipse the PC market over the next several years," according to a copy of Shope's note on the meeting sent to CNET.

Shope himself believes that iPad shipments will surpass expectations this year and next and that demand for PCs will suffer as the tablet market continues to take off.

With Apple seeing improved supply and rising demand for its tablet, the analyst is forecasting iPad sales of 8.1 million for Apple's third fiscal quarter, ending in June, a jump of 72 percent from the same quarter last year. That estimate compares with only 4.69 million iPads that Apple sold during its second quarter when some analysts had been eyeing sales of anywhere from 5 million to 9 million.

But Apple faced challenges trying to ramp up enough supply of the iPad 2 to keep up with demand. J.P. Morgan analyst Mark Moskowitz also believes that second-quarter sales of the iPad were lower than expected due to timing issues, pointing to a statement from Apple that it was facing the "mother of all backlogs."

The iPad 2 debuted in early March and went on sale later that month.

Apple management told Shope that they've continued to work to meet iPad demand and that they were making as many devices as they could."

Also in the meeting were Apple's retail head Ron Johnson and Apple chief financial officer Peter Oppenheimer, who added to the air of optimism by touting the long-term prospects of the iOS ecosystem in general and the iPhone in particular.

Though some Apple investors have been concerned over the possibility that the company won't refresh the iPhone until later in the year, demand for the iPhone 4 continues to be high both in the U.S. and abroad.

Apple now has 200 carriers for the iPhone, up from 186 at the end of the March quarter, noted Shope, and is seeing heavy demand for the phone from its vast network of Apple stores. In a further retail push, the company plans to open another 50 stores annually this year and beyond and revamp its existing stores.