how to send two dimensional array from javascript to server side(c#)

Javascript array cannot be recognized by C#. So, you need to do a trick to serialize the javascript array to a string so that the string can be deserialized in C#.

You can use your custom serialization to convert an array to a string.
In the example I follow the json string, but you can use any logic.

<script language="javascript">
skillArray = new Array(5)

skillArray [0] = new Array(2)
skillArray [0][0] = "Jon"
skillArray [0][1] = "DOT.NET"

skillArray [1] = new Array(2)
skillArray [1][0] = "Tim"
skillArray [1][1] = "C++"

skillArray [2] = new Array(2)
skillArray [2][0] = "Dan"
skillArray [2][1] = "C"

skillArray [3] = new Array(2)
skillArray [3][0] = "Alex"
skillArray [3][1] = "Java"

skillArray [4] = new Array(2)
skillArray [4][0] = "Robert"
skillArray [4][1] = "Perl"

var s='';
for (i=0;i<skillarray.length;>  for (j=0;j<2; j++) {
     if(j==0)
       s += '"' + skillArray[i][j] + '"' + ':';
     else
       s += '"' + skillArray[i][j] + '"';
  }
  s += ",";
}
alert(s);
</script>

So the string will look like
"Jon":"DOT.NET","Tim":"C++","Dan":"C","Alex":"Java","Robert":"Perl"

User Ajax to send the string to C# (code behind).
User split function to split first the primary substring
"Jon":"DOT.NET"
"Tim":"C++"
"Dan":"C"
"Alex":"Java"
"Robert":"Perl"

Now use a loop to iterate each element and split each element with ":"
Thus you can create a 2 dimensional array in C# same as javascript.

cheers