How to make a utility class or function that can be shared?

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If you are using the Pro version, see section 2 'Groovy Script Library' on http://www.soapui.org/Scripting-Properties/scripting-and-the-script-library.html

If not you can try the following technique. Put the following code in your Project Load script:

class MyClass {
    def myMethod() {
    // do stuff    
    }
}

project.metaClass.MyClass = new MyClass()

Then in your Mock Service scripts you can call the method like this:

mockRunner.mockService.project.MyClass.myMethod()