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Students at Yale University last spring. A generation ago, it was rare for even highly competitive colleges to offer places to fewer than 20 percent of their applicants.CreditChristopher Capozziello for The New York Times

Enrollment at American colleges is sliding, but competition for spots at top universities is more cutthroat and anxiety-inducing than ever. In the just-completed admissions season, Stanford University accepted only 5 percent of applicants, an all-time low among the most prestigious schools, with the odds nearly as bad at its elite rivals.

Deluged by more applications than ever, the most selective colleges are, inevitably, rejecting a vast majority, including legions of students they once would have accepted. Admissions directors at these institutions say that most of the students they turn down are such strong candidates that many are indistinguishable from those who get in.

Isaac Madrid applied to 11 colleges, a scattershot approach that he said is fairly typical at his private high school, Bellarmine College Preparatory in San Jose, Calif. Students there are all too aware of the long odds against getting into any particular elite university. “It was a crazy amount of work and stress doing all those essays by the deadline and keeping up my schoolwork, and waiting on the responses, and we had more than $800 in application fees,” he said.

Mr. Madrid, 18, got a taste of how random the results can seem. He was among the 95 percent turned away by Stanford, but he got into Yale, which he plans to attend, and he admitted having no real insight into the reasons for either decision.

Bruce Poch, a former admissions dean at Pomona College in Claremont, Calif., said he saw “the opposite of a virtuous cycle at work” in admissions. “Kids see that the admit rates are brutal and dropping, and it looks more like a crapshoot,” he said. “So they send more apps, which forces the colleges to lower their admit rates, which spurs the kids next year to send even more apps.”

For most of the past six decades, overall enrollment boomed, while the number of seats at elite colleges and universities grew much more slowly, making them steadily more selective. Enrollment peaked in 2011, and it has dropped a bit each year since then, prompting speculation that entry to competitive colleges would become marginally easier. Instead, counselors and admissions officers say, the pool of high-achieving applicants continues to grow, fed partly by a rising number from overseas.

At the same time, students send more applications than they once did, abetted by the electronic forms that have become nearly universal, and uniform applications that can make adding one more college to the list just a matter of a mouse click. Seven years ago, 315 colleges and universities accepted the most widely used form, the Common Application; this year, 517 did.

Students applying to seven or more colleges made up just 9 percent of the applicant pool in 1990, but accounted for 29 percent in 2011, according to surveys by the National Association for College Admission Counseling, and counselors and admissions officers say they think the figure has gone higher still. While people havelavished attention on a Long Island teenager who was accepted by all eight Ivy League colleges, admissions professionals say it is remarkable that anyone would apply to all eight.

The University of California, Los Angeles, the national leader in applications, had 106,000 requests for undergraduate admission, up from 55,000 in 2005. This year, for the first time, U.C.L.A. and the University of California, Berkeley, may have admitted fewer than 20 percent of their applicants.

“For most kids, this really used to be a regional process, but they have access to so much information online now, so every school seems local,” said Richard H. Shaw, the dean of undergraduate admission at Stanford. Admissions directors at several top Eastern colleges agreed, saying that they now received more applications from California than any other state, which would have been unthinkable a few years ago.

Some of them also pointed to colleges’ increasingly aggressive outreach to prospective students, with mailings, emails and advertising — some of it well intentioned, and some of it more cynical.

“One of the ways that colleges are measured is by the number of applicants and their admit rate, and some colleges do things simply to increase their applicant pool and manipulate those numbers,” said Christoph Guttentag, the dean of undergraduate admission at Duke.

The most competitive small colleges draw comparably accomplished applicants, but far fewer of them relative to their size, so their admission rates are higher. Even so, the acceptance rates at Pomona, Amherst, Harvey Mudd, Bowdoin, Claremont McKenna, Swarthmore, Middlebury, Williams and others were between 10 and 20 percent this year.

Mr. Shaw, the Stanford dean, said he could not predict where the rates would bottom out — in fact, he never expected them to go as low as they have.

“Honestly,” he said, “I’m sort of in shock.”