Mass graves have been unearthed in a south Texas cemetery, most probably containing the bodies of immigrants who died crossing into the US illegally, reports say.

The documents published on Saturday highlight the discovery at Sacred Heart Burial Park in Falfurrias which come as part of a multi-year effort to identify immigrants who have died near the US-Mexico border.

The remote area is often deadly for immigrants from Mexico and Central America who set out on foot amid sweltering temperatures to avoid the nearby US Border Patrol checkpoint.

To me it's just as shocking as the mass grave that you would picture in your head, and it's just as disrespectful. Krista Latham, Forensic anthropologist

Anthropologists Lori Baker and Krista Latham and their students exhumed remains stuffed inside trash bags, shopping bags and body bags, according to the Corpus Christi Caller Times.

In one burial, bones of three bodies were inside one body bag. In another, at least five people in body bags and smaller plastic bags were piled on top of each other.

Skulls also were found in biohazard bags placed between coffins.

Latham, a forensic anthropologist at the University of Indianapolis, called the discovery appalling.

Bodies that were not already skeletonized before burial were found in varying states of decomposition, Baker said.

"To me it's just as shocking as the mass grave that you would picture in your head, and it's just as disrespectful," Latham told the Caller Times.

They exhumed 110 unidentified people from the cemetery in 2013.

This summer, researchers have performed 52 exhumations, but because some remains were stored together, further study will be needed to determine exactly how many bodies have actually been recovered, Baker said.

Researchers have said that some remains were found under small, temporary grave markers bearing the name of local funeral home Funeraria del Angel Howard-Williams.

County officials said they pay the funeral home to handle bodies recovered in remote parts of South Texas.

More than 300 people died crossing through Brooks County alone between 2011 and 2013 - representing more than 50 percent of the deaths in Texas' sprawling Rio Grande Valley.