I like to zip multiple files which are being created dynamically in my web application. Those files should be zipped. For this, i dont want to use any third-party tools. just like to use .net api in c#
http://www.codeplex.com/DotNetZip Source codes are available, so you can see how they do it and write something similiar for yourself
Check out System.IO.Compression.DeflateStream. Youll find a couple of examples on msdn http://msdn.microsoft.com/en-us/library/system.io.compression.deflatestream.aspx
I'm not sure what you mean by not wanting to use thrid party tools, but I assume its that you don't want some nasty interop to programmatically do it through another piece of software.
I recommend using ICSharpCode SharpZipLib
This can be added to your project as a reference DLL and is fairly straightforward for creating ZIP files and reading them.
You could always call a third-party executable like 7-zip with an appropriate command line using the System.Diagnostics.Process class. There's no interop that way because you're just asking the OS to launch a binary.