In yet another sign of its deep slump, J. C. Penney Company said on Wednesday that it would close 33 stores across the country and shed about 2,000 jobs.

The company said in a statement that the closings and resulting job cuts would save about $65 million a year.

One of the oldest retailers in the nation, J. C. Penney has undergone considerable management and investment turmoil in the last few years. It fired one chief executive, Ron Johnson, and then brought back his predecessor, Myron E. Ullman III. It tried a new retail strategy, which alienated core customers, and reverted to its old strategy. Its stock has plummeted nearly 80 percent in the last two years.

In Wednesday’s announcement, Penney said it was closing “underperforming” stores. But some analysts and industry experts said that with 1,100 locations and such extensive difficulties, shedding 33 stores would not be enough to move the needle on the company’s performance.