The bodies were found inside the family's home in the 1000 block of South 11th Street around 8 p.m. Thursday.
Arkansas State Police have taken over the investigation and released little information at this time.
KARK is Little Rock is reporting the deceased are 40-year-old Bobby "Chino" Galbraith along with a 4-year-old and 6-year-old. The identities of the children have not been released.
An infant was also found inside the home, according to the Arkadelphia Siftings Herald. The baby was uninjured.
According to the Siftings Herlad, the bodies were discovered by Galbraith's wife.
Investigators on the scene described the investigation as a triple homicide, according to Berry.
According to neighbors, Galbraith was a well-known tattoo artist.