For Android 5.0, if you want to set it directly into a style use:

<item name="android:elevation">0dp</item>
and for Support library compatibility use:

<item name="elevation">0dp</item>
Example of style for a AppCompat light theme:

<style name="Theme.MyApp.ActionBar" parent="style/Widget.AppCompat.Light.ActionBar.Solid.Inverse">
    <!-- remove shadow below action bar -->
    <!-- <item name="android:elevation">0dp</item> -->
    <!-- Support library compatibility -->
    <item name="elevation">0dp</item>
</style>
Then apply this custom ActionBar style to you app theme:

<style name="Theme.MyApp" parent="Theme.AppCompat.Light">
    <item name="actionBarStyle">@style/Theme.MyApp.ActionBar</item>

　　<item name="actionBarSize">@dimen/actionbar_size</item>

</style>

For pre 5.0 Android, add this too to your app theme:

<!-- Remove shadow below action bar Android < 5.0 -->
<item name="android:windowContentOverlay">@null</item>

或者

<android.support.design.widget.AppBarLayout xmlns:android="http://schemas.android.com/apk/res/android"

    xmlns:app="http://schemas.android.com/apk/res-auto"

    android:id="@+id/appbar"

    android:layout_width="match_parent"

    android:layout_height="wrap_content"

    app:elevation="0dp"

    android:theme="@style/ThemeOverlay.AppCompat.Dark.ActionBar">

    <android.support.v7.widget.Toolbar

        android:id="@+id/toolbar"

        android:layout_width="match_parent"

        android:layout_height="wrap_content"

        android:background="?attr/colorPrimary"

        app:popupTheme="@style/ThemeOverlay.AppCompat.Light">

    </android.support.v7.widget.Toolbar>

 </android.support.design.widget.AppBarLayout>