nowhere have you inserted floor 0 into upList,

anotherFloor = (Integer)upList.get(0);
firstElement = anotherFloor.intValue();

so anotherFloor will be null
and anotherFloor.intValue() will throw a null pointer exception
nothing strange here (except perhaps your expectation that it won't)

But I do add it..

upList.add((Integer)theFloor appears just before the code you quote.

Any comments or thoughts?

No, get(0) returns the first item in the list.

The problem is in your Elevator constructor. You never initialize
upList. You create a new local upList that gets destroyed when the
constructor returns.

Also, you do not have to cast theFloor when you add it to the list.

U have declared a list inside a constructor whose scope ends at the closing
brace of the constructor,
uplist pointing to nothing ie null. put the reference out of the constructor
and that would work I suppose. Please let me know if it works

Your Code in the constructor should be re-written as
public class  Elevator
{
private LinkedList upList;
public Elevator()
{
//LinkedList upList = new LinkedList(); // This existed before the mod
upList = new LinkedList(); // This is the modified line uplist has been
declared initialize it
}

...............

}

The problem is in ur Elevator Constructor
Here is the corrected code

import java.util.*;

public class  Elevator
{
private LinkedList upList;
public Elevator()
{
upList = new LinkedList();
}

public void  insertUp (int floor)
{
Integer theFloor;
theFloor = new Integer(floor);
//System.out.println (theFloor);
Integer anotherFloor;
anotherFloor = new Integer(0);
int firstElement;
upList.add((Integer)theFloor);
anotherFloor = (Integer)upList.get(0);
firstElement = anotherFloor.intValue();
}

public int  getFirstFloor()
{
Integer ObjectFirstFloor =
(Integer)upList.get(0);
int firstFloor = ObjectFirstFloor.intValue();
return firstFloor;
}

Please remove the Linked List in teh constructor.

_public Elevator()
_{
__LinkedList upList = new LinkedList();

_}

In the constructor instead of
__LinkedList upList = new LinkedList();

use
upList = new LinkedList();