Use attribute app:elevation="0dp" to your Toolbar or AppBarLayout to remove the shadow.
#. If you are using Toolbar only, then add attribute app:elevation="0dp" to Toolbar.
<android.support.v7.widget.Toolbar
android:id="@+id/toolbar"
android:layout_width="match_parent"
android:layout_height="?attr/actionBarSize"
android:background="?attr/colorPrimary"
app:popupTheme="@style/AppTheme.PopupOverlay"
app:elevation="0dp"/>
#. If you are using AppBarLayout as a container of Toolbar, then add attribute app:elevation="0dp" to AppBarLayout.
<android.support.design.widget.AppBarLayout
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:theme="@style/AppTheme.AppBarOverlay"
app:elevation="0dp">
<android.support.v7.widget.Toolbar
android:id="@+id/toolbar"
android:layout_width="match_parent"
android:layout_height="?attr/actionBarSize"
android:background="?attr/colorPrimary"
app:popupTheme="@style/AppTheme.PopupOverlay" />
</android.support.design.widget.AppBarLayout>
OUTPUT:

UPDATE:
If you want to remove it programmatically then you can use below code:
getSupportActionBar().setElevation(0);
Hope this will help~