STINSON BEACH, Calif.—Time has always been elastic for Grateful Dead fans in thrall to tunes that last more than 45 minutes and shows that go on for hours.

So when the group announced it would mark its 50th anniversary in the summer of 2015 with three final performances, Deadheads took the old-school route, flooding the band’s ticket service here with handcrafted requests rather than clicking online.

Since the shows were announced a month ago more than 60,000 envelopes—many painstakingly adorned with the Dead’s typical psychedelic skulls and skeletons—have poured into a post office box in this picturesque Marin County spot a half-hour from the Golden Gate Bridge. The post office usually receives 7,000 letters a week. “It was a big shock to us,” Jim Harvey, the Stinson Beach postmaster, said of the vivid No. 10 envelopes festooned with Magic Marker sketches and fanciful lettering. “It indicated that the Grateful Dead culture is alive and well.”

The response to the three shows at Soldier Field in Chicago over the July Fourth weekend also blindsided the Dead’s ticket Svengali, Frankie Accardi-Peri. For more than 30 years, Ms. Accardi-Peri has fulfilled the band’s mail-order ticket requests. In January, when envelopes started pouring in, she stored the mail trays in her 24-year-old son’s bedroom. (“I had to use quite a bit of acrobatics in order to get to my bed,” Jesse Peri said.) With more than 100 overflowing trays piling up, Ms. Accardi-Peri realized she needed a hand—many hands. After a few phone calls, help was on the way. She moved the operations to a bigger house and expanded her staff to 60 people, from six.

Most music fans—even the Grateful Dead’s colorful and idiosyncratic enthusiasts—turn to the Internet or Ticketmaster rather than fuss with money orders and self-addressed stamped envelopes. “People don’t do mail order anymore,” Ms. Accardi-Peri said. But “all of a sudden, I can sell out the stadium five times over.”