Thanks icktoofay, 
I tried using HttpWebRequest and HttpWebResponse. 
When I request for URL by passing the Credentials like UserName And Password.
I will get the Session Id Back in the Response.
After getting that Session Id, How to Move Further.
The authenticated user are tracked using credentials/cookies. I'm Having the Exact Url of the File to be downloaded and credentials. If you want to use Cookies I will. I need to read the File Data and write/save it in a Specified Location.
The code I'm using is;
string username = "";
string password = "";
string reqString = "https://xxxx.com?FileNAme=asfhasf.mro" + "?" + 
             "username=" + username + &password=" + password;
byte[] requestData = Encoding.UTF8.GetBytes(reqString);
string s1;
CookieContainer cc = new CookieContainer();
var request = (HttpWebRequest)WebRequest.Create(loginUri);
request.Proxy = null;
request.CookieContainer = cc;
request.Method = "POST";
HttpWebResponse ws = (HttpWebResponse)request.GetResponse();
Stream str = ws.GetResponseStream();
//ws.Cookies
//var request1 = (HttpWebRequest)WebRequest.Create(loginUri);
 byte[] inBuf = new byte[100000];
int bytesToRead = (int) inBuf.Length;
int bytesRead = 0;
while (bytesToRead > 0) 
{
    int n = str.Read(inBuf, bytesRead,bytesToRead);
    if (n==0)
    break;
    bytesRead += n;
    bytesToRead -= n;
}
FileStream fstr = new FileStream("weather.jpg", FileMode.OpenOrCreate, 
                                     FileAccess.Write);
fstr.Write(inBuf, 0, bytesRead);
str.Close();
fstr.Close();