Execute javascript function after asp.net postback without Ajax

You should rather use the ScriptManager class, since the Page.ClientScript property is deprecated...

The ClientScriptManager class is new in ASP.NET 2.0 and replaces Page class methods for managing scripts that are now deprecated.
Reference: MSDN - Page.ClientScript Property

The advantage with ScriptManager is that it works with asynchronous postbacks, so if you are using AJAX it will not work with the ClientScriptManager.

Your code would look like this:

ScriptManager.RegisterStartupScript(this, this.GetType(), "ShowPopup", "showCheckOutPopIn('Livraison',556);", true);

Note also that if you are using AJAX and have a piece of javascript code, that you want executed on multiple postbacks, then you should refer to your UpdatePanel in the firstargument e.g.:

ScriptManager.RegisterStartupScript(MainUpdatePanel, typeof(string), "ShowPopup", "showCheckOutPopIn('Livraison',556);", true);