Broadway stagehands went on strike yesterday, shutting down more than two dozen plays and musicals on what is the most popular theatergoing day of the week.

Picket lines went up at theaters throughout the Times Square area. The first show to be affected was “Dr. Seuss’ How the Grinch Stole Christmas! The Musical,” a holiday attraction for families that had an early 11 a.m. matinee.

A spokesman for Local One, the stagehands union, declined comment on the work stoppage.

A spokeswoman for the League of American Theatres and Producers, Lisa Linden, said the group had not heard from the union regarding the job action. “It would be shocking if they would hurt the theatergoing public by shutting down Broadway without notice,” she said.

The League and Local One have been in negotiations for more than three months, wrangling over work rules and staffing requirements, particularly requirements governing the expensive process of setting up a show.

Local One, which has been working without a contract since the end of July, was told Friday by its parent union, the International Alliance of Theatrical Stage Employees, to begin the walkout yesterday.

Eight Broadway shows will not be affected by the strike, as they are playing in theaters with separate Local One contracts. They are “Young Frankenstein,” “Mary Poppins,” “Xanadu,” “The 25th Annual Putnam County Spelling Bee,” “Mauritius,” “Pygmalion,” “The Ritz,” and “Cymbeline.” Off-Broadway shows will also keep running.

But among the shows shut by the walkout are such popular attractions as “Wicked,” “The Phantom of the Opera,” “Rent,” “Les Miserables,” “Monty Python’s Spamalot,” and “Mamma Mia!”

On Thursday, after two days of contentious negotiations, the local got its parent union’s permission to strike.

November has been an exceptionally busy month for Broadway, with the opening of such plays as Tom Stoppard’s “Rock ‘n’ Roll,” “Cyrano,” starring Kevin Kline, and Mel Brooks’ “Young Frankenstein.” Still to come before Christmas are such productions as “The Farnsworth Invention,” by Aaron Sorkin, Disney’s “Little Mermaid,” and a revival of Harold Pinter’s “The Homecoming.” Broadway traditionally does well in December, particularly in the week between Christmas and New Year’s, normally the busiest of the year.

In March 2003, more than a dozen Broadway shows went dark after musicians went on a four-day strike, costing the city millions of dollars in lost revenue. Earlier this year, the musicians agreed to a new three-year contract.

The 3,000-member stagehands union, which has between 350 and 500 members working on Broadway at any given time, contends it could find employment for many of its people in television or film if a work stoppage occurs.