The idea of a physical mark.. a chip implanted beneath the skin.. or some other methodology.. came out of a more modern view caused by recent books written by various men and not truly from Scripture. The idea of a Biblical "mark", is a symbolic metaphor which carries the meaning of one who is under authority of another or it can mean to take note of, such as in these verses:
Rom_16:17 Now I beseech you, brethren, mark them that are causing the divisions and occasions of stumbling, contrary to the doctrine which ye learned: and turn away from them.
Php_3:17 Brethren, be ye imitators together of me, and mark them that so walk even as ye have us for an ensample.
Obviously, this does not mean a physical mark but a mental notation by the viewer.
In the book of Revelation, the "mark" of the Beast is unlikely to be physical because it would be impossible to implement such a physical alteration to all that will worship the Beast in such a short span of time. Rather, this should be understood as individuals who have been given authority by the Beast because they have professed allegiance to him. The idea of the "mark" of the Beast should be understood as in opposition to those who have been "sealed" by God.
Rev_7:3 saying, Hurt not the earth, neither the sea, nor the trees, till we shall have sealed the servants of our God on their foreheads.
Notice here, the location of the "seal" is said to be in the same location as the "mark", which is upon their forehead.
Now we know, as believers, that we too are "sealed" and we know that we carry no physical mark of this "seal".
2Ti_2:19 Howbeit the firm foundation of God is standing, having this seal, The Lord knows them that are his: and, Let every one that names the name of the Lord depart from unrighteousness.
This is the perfect example verse for our discussion. Note that it says, the Lord knows them that are His. The Beast shall know those that are his. The Lord knows those that are not His. The Beast knows those that are the Lord's. No physical mark needed.
Also, remember these verses, which demonstrate a non-physical sealing of God's own.
2Co_1:22 who also sealed us, and gave us the earnest of the Spirit in our hearts.
Eph_1:13 in whom ye also, having heard the word of the truth, the gospel of your salvation,--in whom, having also believed, ye were sealed with the Holy Spirit of promise,
Eph_4:30 And grieve not the Holy Spirit of God, in whom ye were sealed unto the day of redemption.
Hope this will be of help. God bless.