How to provide shadow to Button

Use this approach to get your desired look.
button_selector.xml :

<selector xmlns:android="http://schemas.android.com/apk/res/android">
<item>
    <layer-list>
        <item android:right="5dp" android:top="5dp">
            <shape>
                <corners android:radius="3dp" />
                <solid android:color="#D6D6D6" />
            </shape>
        </item>
        <item android:bottom="2dp" android:left="2dp">
            <shape>
                <gradient android:angle="270" 
                    android:endColor="#E2E2E2" android:startColor="#BABABA" />
                <stroke android:width="1dp" android:color="#BABABA" />
                <corners android:radius="4dp" />
                <padding android:bottom="10dp" android:left="10dp" 
                    android:right="10dp" android:top="10dp" />
            </shape>
        </item>
    </layer-list>
</item>

</selector>

And in your xml layout:

<Button
   android:background="@drawable/button_selector"
   ...
   ..
/>

Here is my button with shadow cw_button_shadow.xml inside drawable folder

<?xml version="1.0" encoding="utf-8"?>
<selector xmlns:android="http://schemas.android.com/apk/res/android">
    <item android:state_pressed="false">
        <layer-list>
            <!-- SHADOW -->
            <item>
                <shape>
                    <solid android:color="@color/red_400"/>
                    <!-- alttan gölge -->
                    <corners android:radius="19dp"/>
                </shape>
            </item>
            <!-- BUTTON alttan gölge
              android:right="5px" to make it round-->
            <item
                android:bottom="5px"
                >
                <shape>
                    <padding android:bottom="5dp"/>
                    <gradient
                        android:startColor="#1c4985"
                        android:endColor="#163969"
                        android:angle="270" />
                    <corners
                        android:radius="19dp"/>
                    <padding
                        android:left="10dp"
                        android:top="10dp"
                        android:right="5dp"
                        android:bottom="10dp"/>
                </shape>
            </item>
        </layer-list>
    </item>

    <item android:state_pressed="true">
        <layer-list>
            <!-- SHADOW -->
            <item>
                <shape>
                    <solid android:color="#102746"/>
                    <corners android:radius="19dp"/>

                </shape>
            </item>
            <!-- BUTTON -->
            <item android:bottom="5px">
                <shape>
                    <padding android:bottom="5dp"/>
                    <gradient
                        android:startColor="#1c4985"
                        android:endColor="#163969"
                        android:angle="270" />
                    <corners
                        android:radius="19dp"/>
                    <padding
                        android:left="10dp"
                        android:top="10dp"
                        android:right="5dp"
                        android:bottom="10dp"/>
                </shape>
            </item>
        </layer-list>
    </item>
</selector>

How to use. in Button xml, you can resize your height and weight

<Button
                android:text="+ add friends"
                android:layout_width="120dp"
                android:layout_height="40dp"
               android:background="@drawable/cw_button_shadow" />

If you are targeting pre-Lollipop devices, you can use Shadow-Layout, since it easy and you can use it in different kind of layouts.

Add shadow-layout to your Gradle file:

dependencies {
    compile 'com.github.dmytrodanylyk.shadow-layout:library:1.0.1'
}

At the top the xml layout where you have your button, add to the top:

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

it will make available the custom attributes.

Then you put a shadow layout around you Button:

<com.dd.ShadowLayout
        android:layout_marginTop="16dp"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        app:sl_shadowRadius="4dp"
        app:sl_shadowColor="#AA000000"
        app:sl_dx="0dp"
        app:sl_dy="0dp"
        app:sl_cornerRadius="56dp"> 

       <YourButton
          .... />

</com.dd.ShadowLayout>

You can then tweak the app: settings to match your required shadow.

Hope it helps.

For android version 5.0 & above

try the Elevation for other views..

android:elevation="10dp"

For Buttons,

android:stateListAnimator="@anim/button_state_list_animator"

button_state_list_animator.xml - https://android.googlesource.com/platform/frameworks/base/+/master/core/res/res/anim/button_state_list_anim_material.xml

below 5.0 version,

For all views,

 android:background="@android:drawable/dialog_holo_light_frame"

My output: