If you use an MVVM pattern to populate the data in the RadTileVIew and want to access the ViewItem's model object via Button, I suggest you use a Command. So, when the user clicks a button in the View, a command on the ViewModel will execute to perform the requested action.
I'm attaching a sample project that demonstrates this approach. The scenario is very simple - we have a RadTileView bound to a ViewModel and in each RadTileViewItem we have a Button. On a button click, the Description Property in the ItemViewModel is changed.
I hope this information helps.
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