Hi,
If you use basic types it shouldn't be a problem. See http://msdn.microsoft.com/en-us/library/ms973893.aspx What happens if you just try ?
You still may want to give some details about this class. For example if this is just to store some simple properties my personal preference would be likely to create a class that just stores each of its properties in a separate session variable under the hood rather than to store the object itself in a single session variable. For example see http://www.codeproject.com/Articles/2404/Create-Typed-Session-State-in-ASP-NET