The two geneologies of Jesus

 This apparant contradiction has been dealt with by many apologists in many of their apologetics website

1. http://www.complete-bible-genealogy.com/genealogy_of_jesus.htm
Genealogy of Jesus
"Jesus' genealogy can be found at two places in the Bible:

1. Matthew's gospel (Mat 1:2-16). Starts with Abraham and lists his descendants all the way down to Jesus. There are 41 generations in total, divided into 3 sections as follows:
   
   

   1.	Abraham	- David	(from Abraham to David)
   2.	David	- Josias	(from David until the carrying away into Babylon)
   3.	Jechonias	- Jesus	(from the carrying away into Babylon unto Christ)

   
   Each section contains 14 generations. Note, that David is counted twice: Once at the end of the first section, then once again at the beginning of the second section. This explains how 41 generations are divided equally into three. See Mat 1:17 for further explanation.
   
   
2. Luke's gospel (Luk 3:23-38). This genealogy starts with Jesus and follows his line up until God. There are 77 generations mentioned in total.

In each of the two genealogies every name is different up until David with the exception of Joseph, Zorobabel and Salathiel. Therefore it is practically impossible to reconcile them by matching the persons and say, they are just listed by their different names (as we've seen many times before in the Bible). This suggests that the two genealogies do not trace the same lineage.
Since you can trace a person's ancestors through their father, and also through their mother (and the two genealogies should naturally be different) it is easy to come to the conclusion that one of the two genealogies in the gospels must list Jesus' ancestors through his "father", while the other one lists them through his mother."
2.  http://www.soundofgrace.com/piper81/022281e.htm
Now comes the genealogy and a whole bunch of questions leap off the page into our

minds. In Matthew and Mark the account of Jesus' temptations comes right after the account

of his baptism, but Luke inserts the genealogy between these two accounts. Why? Luke's

genealogy goes all the way back to Adam while Matthew's goes back only to Abraham.

Why? The names in the two genealogies from Jesus back to king David are almost all

different. Why? And are we to imagine that man is only as old as the number of years that

can be calculated for all these names back to Adam? Let's look at some answers to these

four questions very briefly in reverse order.

    1) No, we need not think that the sum of each of these person's life equals the age of man.

The main reason is that in Jewish lineage lists "son" was often used also in the sense of

"grandson" or even "descendant." In fact in Luke 3:24-38 the word "son" does not even occur

in Greek. It simply says Heli was "of Matthat, of Levi, of Melchi" and so on. What matters in

a lineage is not that every member be included but that the genuine line of descent be

maintained.

    We know from Matthew's genealogy that some names were left out. In Matthew 1:8 it

says Joram was the father of Uzziah; but in 1 Chronicles 3:11 there are three other names

listed between these two. One of the reasons for this is so that Matthew could have three

equal groups of 14 names each (Matthew 1:17). The same motive might have been at work in

Luke's genealogy because there appear to be 11 groups of 7 names each with all the

important figures either at the beginning or end of a group. But Luke doesn't draw attention to

this like Matthew does so we shouldn't press it. So I don't think we are bound to Ussher

chronology which makes man about 6000 years old. Just how old man is is a problem we'll

leave for another time.

    2) Why, when you compare Matthew's genealogy with Luke's between David and Jesus

are they almost completely different? All the names but two are different. A major

commentary published in 1978 by I. H. Marshall says, "It is only right therefore to admit that

the problem caused by the existence of the two genealogies is insoluble with the evidence

presently at our disposal" (p. 159). What he means is not that the two are in unresolvable

conflict. There are suggested solutions, but we just don't know enough to be sure these

solutions are the proper ones. I'll just mention two. One suggestion is that from David to

Jesus, Matthew "gives the legal descendants of David--the men who would have been legally

the heir to the Davidic throne if that throne had continued--while Luke gives the descendants

of David in that particular time to which finally Joseph, the husband of Mary, belonged"

(Machen, Virgin Birth, p. 204). So, for example Luke says in 3:31 that the son of David was

Nathan (2 Samuel 5:14) while Matthew in 1:6 says the son of David was Solomon, who was

heir to the throne. The two lines could easily merge whenever one of Nathan's descendants

became the rightful heir to the throne.

    The other suggested solution is that Luke gives Mary's genealogy and Matthew gives

Joseph's as Jesus' legal father. The key to this interpretation is extending the parenthesis of

verse 23 to include Joseph. So it would read, "Jesus was about 30 years old being the son

(as was supposed of Joseph) of Heli etc." By including "of Joseph" in the parenthesis the

point is made that Jesus is really the son of Mary not Joseph and Heli is his grandfather

(Mary's father). Both of these solutions are possible; the first is more probable; but neither

can be proved.