But what he could not have expected is that his brush with the law would be immortalised by Shakespeare as the inspiration for Measure for Measure, the playwright's tale of moral degradation and sexual hypocrisy.
Beeston, a jobbing Elizabethan actor who belonged, with Shakespeare, to one of a number of fiercely competitive theatre companies, issued a forthright denial that he had attacked Margaret White, a cloth worker's widow, on Midsummer's night, leaving her pregnant.
Research into Elizabethan court records has revealed evidence that suggests Shakespeare drew on the experience of Beeston and his chaotic appearance before Bridewell Court in writing Measure for Measure, which features a rapist and riotous court scenes.
Documents recounting the appearance of Beeston, who went on to become one of 17th century London's leading impresarios and was not averse to boasting of his sexual prowess, relate how his colleagues disrupted a hearing as he protested his innocence.
Duncan Salkeld, a senior lecturer in English at University College Chichester, who has spent nine years scouring the archive, said: "It is inconceivable that Shakespeare did not know either of the allegations against Beeston or the hearing that took place.
"It is also possible that he was at the hearing itself. We know Beeston's 'confederates' were at the court, where they behaved extremely badly. It therefore seems at least likely that this episode was in Shakespeare's mind when Measure For Measure was written two years later."
Although it is not known whether Beeston and Shakespeare were close friends, they were both members of the Lord Chamberlain's Men theatre troupe during the 1590s. But Beeston changed abruptly to a rival company, the Earl of Worcester's Men, in August 1602, barely a month after the rape allegation was made, suggesting he may have been forced out.
The evidence of Beeston's prosecution is contained in the "Minute Books" of the court of governors of Bridewell prison, a notorious establishment on the banks of the Thames at Blackfriars, and Bethlem Hospital, aka Bedlam. They are held at the Bethlem Royal Hospital Archives in Beckenham, south London.
The documents relate how White accused Beeston, who by 1617 had his own theatre company, of "forciblie" having sex with her, boasting that he had slept with "a hundred wenches". The record states how Beeston appeared on that day with his fellow "plaiers" and that the group "did very vehemnentlie demeane themselves ... and much abused the place".
The debacle seems to have worked in Beeston's favour. Despite ruling that there were grounds for Beeston to be "greatlie suspected to have committed the facte" and that he be tried for rape, it seems the allegation was allowed to lie on the court files.
Experts say the documents, published in the Review of English Studies, offer a glimpse into the events surrounding Shakespeare when he was writing his plays and how they may have affected his thinking.
Measure for Measure features a character called Lucio who admits making a prostitute pregnant. One of the protagonists, Angelo, threatens to rape another character. The play also contains a number of prison scenes, including one in which a character is sent to jail for "correction and instruction" - the motto of Bridewell.