In a rare public expression of dissent, Chief Justice Warren E. Burger yesterday objected to the admission of two lawyers to practice before the Supreme Court.

Burger's written dissent was unusual, since attorneys are admitted to the Supreme Court bar almost rroutinely. What was even more unusual, however, was that Burger made his objections public, departing from a procedure that systematically shields rejected applicants from public embarrassment.

Both attorneys, Yale H. Iverson of Des Moines, Iowa, and William Frederick Olson of El Paso, Texas, had been reprimanded by judicial authorities in their home state. Both were admitted yesterday to practice before the Supreme Court, but Burger - dissenting from his eight collegues, - said the two did not meet the court's standard that applicants' "personal and professional character appear to be good."

Supreme Court employes said it was the first time they had heard of a justice dissenting publicly on a bar admission in more than 20 years. Even in rare instances when applicants are rejected outright the rejection is not made public, so that no one but the attorney and the Supreme court clerk knows he ever applied.

In his terse opinion opposing Iverson's admission, Burger said the Des Moines attorney's application "is one in the familiar pattern of lawyers who have been disciplined by their state and then seek admission to this court so they can hang in their offices' evidence' that they have been cleansed of the stigma of their misconduct."

Burger pointed out that Iverson had been eligible to apply for admission to the Supreme Court bar for 12 years, but waited until a few months after his July 1978 reprimand to apply for the Supreme Court bar membership.

Iverson,reached at his Des Moines office, said "it simply is not true" that he was applying for Supreme Court membership in order to have a prestigious certificate to offset his earlier reprimand by the Iowa Supreme Court. Iverson said dhe had an appeal currently pending before the Supreme Court, and by the court's own rules only bar members are allowed to practice cases before it.

"I'm sorry that the Chief Justice took that view, especially since I have an appeal pending before his court," Iverson said. He said Burger's dissenting opinion "is about as nice as somebody telling you you've got diarrhea . . . It's not quite the same thing as my mother telling me she's not my mother."

Iverson was "severly disciplined" in his state for improperly handling three crininal appeals. Olson, the other lawyer who drew Burger's ire, was censured by the Arizona state bar in 1976 for taking a client's car to keep itfrom being garnisheed in a bankruptcy suit.

The Supreme Court bar generally is undiscriminating, requiring only that applicants pay a $25 fee and have been admitted to practice before the highest court in their home state for at least three years. About 150,000 lawyers are currently members of this bar, although most will never have occasion to practice a case before the Supreme Court.

One Supreme Court source said that while both Iverson and Olson were admitted yesterday, Burger's public dissent and written opinion could be a signal that admission to the Supreme Court bar will no longer be an automatic process. It could also indicate, the source said, that unqualified and questionable applicants may no longer have their rejections protected by the court's traditional veil of secrecy. CAPTION: Picture, CHIEF JUSTICE WARREN BURGER. . . departs from tradition