The Samaritans observes the commandment of the Berit Milla-circumcision as it is in the Torah:
“And in the eighth day the flesh of his foreskin shall be circumcised” (Leviticus 12:3)
On the eighth day after the birth of a boy, the circumcision takes place in the early hours of the morning (around 7:00am)- usually in order to let people have the chance to participate the holy ceremony and to prevent any chance of any unexpected events that would postpone it, as well as 
a remembrance of ancient days, in which the Samaritans were persecuted and had to fulfilled the ceremony in secret. There is a well-known story, in Samaritan chronicles, of the Byzantines period concerning the Priest Ekbon, who was caught on his way to circumcise his son. The roman guard named Garmon, smiled to the little boy and let his father pass. The most known Samaritan scholar Markeh (Markus)– decided to mention this good deed, and added his name to his poem, still in use in this days, for a blessing :
“References to the good Garmon, the Roman guard”.
The circumcision ceremony (Berit Milla), normally takes place on the eighth day without any postpone, unless the newborn life is in danger, in this case as well as if he was placed inside an incubator by doctors. Only in these types of cases, the circumcision will take place on the eighth day after the newborn is taken out of the incubator.
The circumcision ceremony, is overseen by the local High Priest, while the circumcision itselfis made by a Jewish circumcizer (Mohel) or an Arabic doctor, due to the fact that there are no Samaritan circumcizers among the Samaritans these days. In ancient times, the circumcizer used to be a Samaritan priest. It is a joyous occasion where the guests receive refreshment by the family of the baby, and those present, give donations to the newborn’s mother.