C# - how to do multiple web requests at the same time

It is unlikely that your service calls are CPU-bound. So spinning up more threads to handle the load is maybe not the best approach-- you will get better throughput if you use async and await instead, if you can, using the more modern HttpClient instead of HttpRequest or HttpWebRequest.

Here is an example of how to do it:

var client = new HttpClient();

//Start with a list of URLs
var urls = new string[]
    {
        "http://www.google.com",
        "http://www.bing.com"
    };

//Start requests for all of them
var requests  = urls.Select
    (
        url => client.GetAsync(url)
    ).ToList();

//Wait for all the requests to finish
await Task.WhenAll(requests);

//Get the responses
var responses = requests.Select
    (
        task => task.Result
    );

foreach (var r in responses)
{
    // Extract the message body
    var s = await r.Content.ReadAsStringAsync();
    Console.WriteLine(s);
}