I know it is an old question, but people keep asking it, trying to do this kind of thing (explicitly spawning threads while processing a servlet request) all the time... It is a very flawed approach - for more than one reason... Simply stating that Java EE containers frown upon such practice is not enough, although generally true...
Most importantly, one can never predict how many concurrent requests the servlet will be receiving at any given time. A web application, a servlet, by definition, is meant to be capable of processing multiple requests on the given endpoint at a time. If you are programming you request processing logic to explicitly launch a certain number of concurrent threads, you are risking to face an all but inevitable situation of running out of available threads and choking your application. Your task executor is always configured to work with a thread pool that is limited to a finite reasonable size. Most often, it is not larger than 10-20 (you don't want too many threads executing your logic - depending on the nature of the task, resources they compete for, the number of processors on your server, etc.) Let's say, your request handler (e.g. MVC controller method) invokes one or more @Async-annotated methods (in which case Spring abstracts the task executor and makes things easy for you) or uses the task executor explicitly. As your code executes it starts grabbing the available threads from the pool. That's fine if you are always processing one request at a time with no immediate follow-up requests. (In that case, you are probably trying to use the wrong technology to solve your problem.) However, if it is a web application that is exposed to arbitrary (or even known) clients who may be hammering the endpoint with requests, you will quickly deplete the thread pool, and the requests will start piling up, waiting for threads to be available. For that reason alone, you should realize that you may be on a wrong path - if you are considering such design.
A better solution may be to stage the data to be processed asynchronously (that could be a queue, or any other type of a temporary/staging data store) and return the response. Have an external, independent application or even multiple instances of it (deployed outside your web container) poll the staging endpoint(s) and process the data in the background, possibly using a finite number of concurrent threads. Not only such solution will give you the advantage of asynchronous/concurrent processing, but will also scale because you will be able to run as many instances of such poller as you need, and they can be distributed, pointing to the staging endpoint.
HTH