The workers were inadvertently exposed to a low dose of ionising radiation as they were repairing a leaking tank on a Trident nuclear weapons submarine at the same time a nearby reactor was undergoing trials.
The Ministry of Defence (MoD) said no one was harmed in the incident, which took place in August 2012.
Details were revealed in documents released to the campaign group Nuclear Information Service by the Office for Nuclear Regulation (ONR) under Freedom of Information legislation.
A report identified “poor communication” and “a lack of understanding of the magnitude of the hazards present when operating a reactor” as contributing factors.
“There was a prolonged and repeated failure of the ships staff to understand and control the radiological hazard that they were creating”, it said.
Other documents obtained by the group reveal that in April 2012 a training team was allowed to visit a submarine and enter a radiation exclusion zone without being issued with dosimeters, devices that measure exposure to ionising radiation.
In February 2013 a sailor working on a submarine at the base left it with a sponge bung without having it checked for contamination.
A forth incident in December 2013 involved a Babcock employee who removed some grills from an external tank and put his head inside, exposing himself to a small dose of radiation.
SNP defence spokesperson Brendan O’Hara MP said: “The MoD - once again - stands accused of a very poor approach to radiation safety at the Faslane base.
“When it comes to protecting our armed forces personnel, the contractors working at the base, as well as the wider community, nuclear safety must be paramount.
‘’These incidents and how they were subsequently handled, pose real and serious questions , not just about nuclear safety procedures at the base - but also whether the regulator the ONR is doing enough - and quickly enough - to address these concerns.
‘’The MoD must investigate and explain why these failings occur and lay out precisely what it is doing to get it sorted.’’
A MoD spokesman said: “Safety at Clyde naval base is of paramount importance and none of the events in this report caused harm to any member of staff or the public.
“Investigations were carried out and measures put in place to prevent such incidents from occurring again, and we continue to conduct rigorous monitoring as part of our commitment to maintain the highest standards.”