ScrollViewer.HorizontalScrollBarVisibility="Hidden"

<TreeView ScrollViewer.HorizontalScrollBarVisibility="Hidden" Width="145" Name="tree_menu" >
   <TreeViewItem Header="This is a very long root element node text">
      <TreeViewItem Header="this is a very long child element node text" />
   </TreeViewItem>
</TreeView>

<TreeView Name="tree_menu">
    <TreeView.Resources>
        <Style TargetType="{x:Type TreeViewItem}">
            <Setter Property="HeaderTemplate">
                <Setter.Value>
                    <DataTemplate>
                        <TextBlock Width="145"
                                   TextWrapping="Wrap"
                                   Text="{Binding}" />
                    </DataTemplate>
                </Setter.Value>
            </Setter>
        </Style>
    </TreeView.Resources>
    <TreeViewItem Header="This is a very long root element node text">
        <TreeViewItem Header="this is a very long child element node text" />
    </TreeViewItem>
</TreeView>