They range from cremated remains to partial and complete skeletons.
NMS wants expert help to assess details such as age, sex and stature – as well as signs of trauma or disease, which could relate to cause of death.
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Dr Matthew Knight, senior curator of early prehistory at NMS, said it holds Scottish archaeological human remains “from more than 500 sites, comprising approximately 1,500 individuals”.
He said: “Human remains were among the earliest donations to the museum in 1781 and today we continue to collect from archaeological excavations.
"Typically, they are preserved in association with material artefacts from these excavation assemblages.”
He said the remains are preserved “with care and respect”, adding: “The collection is actively researched by museum staff and accredited researchers, and the results from osteoarchaeological and scientific analyses allow us to reveal important insights into the stories of the people from Scotland’s past, including how they travelled, what they ate, how they lived and how they died.”
Documents posted to the Public Contracts Scotland website say NMS is looking for “full osteological identification of archaeological human remains from Scotland spanning the prehistoric to post-medieval periods, with a focus on prehistoric and early medieval”.
This includes verification of previous identification work.
The documents show the majority of the partial or complete skeletons in the collection – more than 888 – date from the medieval period.
Most of the individual skulls also come from the medieval or later medieval periods.
However, many of the remains are far older, with hundreds stretching back into the Bronze and Stone ages.
An estimated 213 of the skeletal remains date from the Mesolithic or Neolithic periods.
In total, there are around 1,479 partial or complete skeletons in the collection, and around 174 skulls and 217 cremation deposits.
NMS is also recruiting specialists to help with the registration of 250 archaeological sites comprising human remains in Scotland, primarily from prehistory.
It said this represents around half of the collection, with the other half previously registered.
This will include outlining site details and summarising the human remains discovered.
Both projects are expected to be completed by the end of June 2023, with an indicative budget of around £40,000 in total.
Dr Knight said: "The two opportunities available to tender will allow us to bring in specialist expertise supporting our ongoing work to augment the documentation of the history of the collection and to develop future programmes of research.
"Ultimately it will enhance our knowledge of those who came before us.”
NMS is spread over five sites, including the National Museum of Scotland on Chambers Street in Edinburgh.
It recently launched a new exhibition exploring the “social and medical history surrounding the dissection of human bodies”, featuring the famous Burke and Hare murders in 1828.