There is an excellent article here that covers the Biblical arguments for, and the common arguments against each point. A few relevant excerpts"
The word baptizo in Greek, translated "baptize" in the New Testaments,
meant to "dip" or "immerse." It is sometimes argued that in Mark 7:4
and Luke 11:38 the word means "to wash by pouring," not "immerse"; but
in those texts the actual meaning (as historical information
substantiates) is to "wash by dipping or immersing in water."
Baptism is specifically stated in the New Testament to represent the
Christian's spiritual union with Christ in His death, burial and
resurrection (Romans 6:3-7), which is remarkably and dramatically
pictured in immersion.
Whenever the act of baptism is described in the New Testament (which is rarely), the one who is baptized actually goes into the
water. Thus, after Jesus was baptized, He "came up out of the water"
(Mark 1:10), and when Philip baptized the Ethiopian eunuch, "they both
went down into the water" (Acts 8:38). These descriptions do not
quite prove complete immersion, however, since they could have stood,
let us say, ankle-deep in water while one of them scooped up some
water and poured it over the other's head. Furthermore, we are not
told in Scripture that we must baptize in exactly the same way as John
The mode used by the early Church in the first few centuries was immersion, with affusion reserved for occasions when immersion was
impossible due to lack of sufficient water, and aspersion used for
individuals too sick or weak for either immersion of affusion.
There is more in the original article, but in summary, the Biblical argument is based on both the meaning of the original Greek word, and also from evidence inferred, but not directly stated in Scripture.
The summary, however, is excellent, in my opinion. The author states:
...Scripture and common sense indicate that the water is not
all-important and that, therefore, other modes may be used as
substitutes in exceptional circumstances. God accepts the believer on
the basis of his faith in Christ and his desire to obey Him, not on
the basis of how much water covered his body when he was baptized.
The doctrine that immersion is the only valid mode of baptism and that
only those so baptized should be admitted into the fellowship of the
Church body would, therefore, appear to be a bit extreme and not based