To use "using" you need to have implementation IDisposable interface, so here is how my ViewModel look like:

namespace UsingExample.ViewModel
{
  using System;
  using System.Windows;

  public class UsingExampleViewModel
  {
    public string UsingExampleTest { get; set; }

    public UsingExampleViewModel()
    {
      using (UsingExampleClassTest aaa = new UsingExampleClassTest())
      {
        aaa.myTest = "rrr";
      }
      UsingExampleTest = "test";
    }
  }

  public class UsingExampleClassTest: IDisposable
  {
    public string myTest { get; set; }

    public void Dispose()
    {
      MessageBox.Show("Die object!");
    }
  }

}

XAML:

<Window x:Class="UsingExample.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:viewModel="clr-namespace:UsingExample.ViewModel"
        Title="MainWindow" Height="350" Width="525">
    <Grid>
        <Grid.Resources>
            <viewModel:UsingExampleViewModel x:Key="UsingExampleViewModel" />
        </Grid.Resources>
        <TextBox DataContext="{StaticResource UsingExampleViewModel}" Text="{Binding UsingExampleTest}"/>
    </Grid>
</Window>

Example project you can download from here.