‘And he causes all, the small and the great, the rich and the poor, the free and the bond, that there be given them a mark on their right hand or on their forehead, and that no man should be able to buy or to sell except the one who has the mark, even the name of the beast or the number of his name.'
The mark on the right hand or on the forehead can be compared to the phylacteries (small leather boxes holding a portion of the Law) worn by the Pharisees (applying literally Deuteronomy 6:8) signifying their submission to God and His Law. This mark of the beast too is a sign of submission, to Rome and the Emperor, and to Roman law.
It parodies the mark given to the people of God and the marking with His name (Revelation 7:3; Revelation 14:1; Revelation 3:12). By this those who receive it acknowledge the Emperor and Rome as having total rights over them. Slaves were commonly marked on their foreheads as a sign of ownership and religious devotees would often deliberately receive some kind of mark to demonstrate their loyalty to their god, so the idea was not uncommon.
There is no reason to assume that this mark is any more physical than the seal on believers, it rather represents submission to the beast and his claims. To bear the mark of the beast was, to the early church, to have sacrificed to Roma and the emperor. To them this bore a stigma that went beyond any other.
But later, under Roman rule, all men would require a certificate that they had sacrificed to the Emperor's image, and it is quite possible that the idea, or some other device, was first used under these early Emperors. Those who had no certificate could (as indeed could those who refused to sacrifice to the emperor) be excluded from normal life by zealous officials or personal enemies, and even denounced by those of other religions (compare on Revelation 2:9), and it would affect their abilities to trade through the guilds which themselves had religious connotations. These certificates themselves were a ‘mark of the beast' and had to carry the official ‘brand'. But such exclusion was quite possible simply for being recognised as a proscribed Christian, a situation applying officially at least from the time of Trajan.
But through the ages this has always been a way by which despots could control people, by utilising control of the means of trade and sources of sustenance. The beast continually reveals his beastliness. And when Christians find themselves suffering as a result of such activity they can take comfort in the thought that it is confirmation that they do not bear the ‘mark of the beast'. That any future anti-Christ would apply similar methods goes without saying. There is nothing new under the sun (Ecclesiastes 1:9).