In the first of a planned month's worth of demonstrations against the policies of the Reagan administration, the speeches and the marches and the burning of President Reagan in effigy went as planned yesterday. But try as they might, no protester could manage to get arrested.

And that quite visibly irritated the three dozen or so mostly female demonstrators who kicked off "A Harvest of Shame," a series of protests aimed at dramatizing opposition to Reagan's reelection by getting demonstrators arrested for committing acts of civil disobedience.

"For the past four years there has been no President in the White House, there has been instead a straw man . . . ," said Liz Seaborn, a 33-year-old District woman whose words signaled the torching of an effigy of Reagan propped up in a washtub in the middle of Pennsylvania Avenue.

The protesters charged that Reagan's programs and policies are moving the world closer to nuclear destruction, dismantling social programs that large numbers of women and children depend upon and threatening women's quest for justice and equality.

"We are anti-Reagan women and we are voting, voting for our lives," the protesters sang as the straw-and-newspaper likeness of Reagan stubbornly refused to burn. After repeated attempts, it finally collapsed into flame and ash. But the throng of U.S. Park and District police on hand did not move to arrest any of the participants.

Despite their best efforts to misbehave, the demonstrators were permitted to do just about anything short of charging the White House gates. For almost 30 minutes, they raced from intersection to intersection near the White House, blocking traffic with their bodies and their banners.

Police responded quickly by rerouting lunchtime motorists around the protesters. They never attempted to break up the impromptu roadblocks or take anyone into custody.

"Could you imagine a group of black demonstrators not getting arrested?" asked Suzette Rowe, a member of the Community for Creative Non-Violence (CCNV), which is organizing the protests, noting the fact that most of yesterday's protestors were white. "This is disgusting."

For more than 10 minutes, the demonstrators danced and sang protest songs in the middle of the intersection of 14th Street and New York Avenue as traffic snarled several blocks deep in two directions. Eventually, the protesters decided to march -- without a permit -- back to the White House for more singing and chanting.

Joe Gentile, a District police spokesman, said none of the protesters was arrested because "they wanted to be arrested to further promote their cause." He added that police also had their hands full with another demonstration.

But CCNV spokesman Mitch Snyder said the Reagan White House was behind the no-arrest policy, thwarting his aim to have at least one protester arrested every weekday until election day.

"People are not allowed to walk up and down the streets of Washington with impunity and parade like that with a police escort," Snyder said. "That was done so the President would not look heavy handed in response to the demands of women when, in fact, he has been heavy-handed to women."

Sonia Johnson, a candidate for president from the Citizens Party and a protest participant, said she was not discouraged by the day's events. Addressing a group of demonstrators in front of the White House, she declared: "The American people aren't stupid and we aren't fools. And we're very angry and will be back every day this month to protest in this place . . . . "