How to create a shadow drop effect around a wpf button like the google button

In the past, I implemented material elevation like this:

public static class UI
{
    private static readonly DropShadowEffect[] sShadows = new[]
    {
        new DropShadowEffect()
        {
            BlurRadius = 5,
            ShadowDepth = 1
        },
        new DropShadowEffect()
        {
            BlurRadius = 8,
            ShadowDepth = 1.5
        },
        new DropShadowEffect()
        {
            BlurRadius = 14,
            ShadowDepth = 4.5
        },
        new DropShadowEffect()
        {
            BlurRadius = 25,
            ShadowDepth = 8
        },
        new DropShadowEffect()
        {
            BlurRadius = 35,
            ShadowDepth = 13
        }
    };

    public static readonly DependencyProperty ElevationProperty = DependencyProperty.RegisterAttached("Elevation", typeof(double), typeof(UI), new FrameworkPropertyMetadata(default(double), FrameworkPropertyMetadataOptions.AffectsRender, null, OnElevationChanged));

    public static double GetElevation(this UIElement element) => element.GetValue(ElevationProperty) as double? ?? default;

    public static void SetElevation(this UIElement element, double elevation) => element.SetValue(ElevationProperty, elevation);

    private static object OnElevationChanged(DependencyObject dependencyObject, object value)
    {
        if (dependencyObject is UIElement element && value is double elevation)
        {
            if (elevation == 0)
            {
                element.Effect = null;
            }
            else
            {
                var effect = CreateElevation(elevation, element.Effect);

                if (effect != null)
                    element.Effect = effect;
            }
        }

        return value;
    }

    private static void MixShadows(DropShadowEffect target, DropShadowEffect other, double balance)
    {
        target.BlurRadius = target.BlurRadius * (1 - balance) + other.BlurRadius * balance;
        target.ShadowDepth = target.ShadowDepth * (1 - balance) + other.ShadowDepth * balance;
    }

    private static Effect CreateElevation(double elevation, Effect source)
    {
        if (elevation < 0 || elevation > 12)
            throw new ArgumentOutOfRangeException("Elevation must be between 0 and 12.", nameof(elevation));

        elevation = Math.Max(0, elevation / 12 * shadows.Length - 1);

        var shadows = sShadows;
        var prevIndex = (int)Math.Floor(elevation);
        var index = (int)elevation;
        var nextIndex = (int)Math.Ceiling(elevation);
        var approx = elevation - index;
        var shadow = shadows[index];
        var modify = false;

        if (approx != 0)
            MixShadows(shadow, approx < 0 ? shadows[prevIndex] : shadows[nextIndex], Math.Abs(approx));

        if (source is DropShadowEffect sourceShadow)
        {
            sourceShadow.BlurRadius = shadow.BlurRadius;
            sourceShadow.ShadowDepth = shadow.ShadowDepth;
            shadow = sourceShadow;
            modify = true;
        }

        shadow.Direction = 270;
        shadow.Color = Color.FromArgb(0xAA, 0, 0, 0);
        shadow.Opacity = .42;
        shadow.RenderingBias = RenderingBias.Performance;

        return modify ? null : shadow;
    }
}

Then,

<Button local:Elevation="2">Elevated button</Button>

Any value between 2 and 12 can be set as the elevation of any UIElement.

You can produce a shadow drop ish effect by changing the BorderThickness some. Try something like this:

<Trigger Property="IsMouseOver" Value="True">
    <Setter TargetName="border" Property="BorderBrush" Value="DarkGray" />
    <Setter Property="Foreground" Value="Black" />
    <Setter Property="BorderThickness" Value="1,1,2,2" />
</Trigger>

Note that doing it this way can mess up your layout a bit, since it changes the total width and height of your button, so other controls around it may "bump around" just a tad when hovering the button.

If you want to play around with proper drop shadow, you can add drop shadow to your button like this:

<Button>
    <Button.BitmapEffect>
        <DropShadowBitmapEffect Color="Black" Direction="320" Softness="1" ShadowDepth="10" Opacity="0.5" />
    </Button.BitmapEffect>
</Button>

EDIT:

As MrDosu commented, BitMapEffect is deprecated so you should probably use Effect instead.

Here's a sample using Effect:

<Trigger Property="IsMouseOver" Value="True">
    <Setter TargetName="border" Property="BorderBrush" Value="DarkGray" />
    <Setter Property="Foreground" Value="Black" />
    <Setter Property="Button.Effect">
        <Setter.Value>
            <DropShadowEffect Color="Black" Direction="320" ShadowDepth="3" BlurRadius="5" Opacity="0.5" />
        </Setter.Value>
    </Setter>
</Trigger>