I'd imagine the "fix" for this would be to wrap the image in a view that contains border radius instead. Eg.
<View style = {{flex: 1, borderRadius: 10}} ><Image style={ {width: 300, height: 100 } } source={{ uri: 'https://placekitten.com/300/100' }}> <Text>SampleText</Text> </Image> </View>

Tried it, unfortunately the images still had no borderRadius applied.

@5in4 did you try it with a more recent RN version?

I managed to get around this by having the Text after the image and setting it to absolute/top:0.

<View style={container}>
  <Image {/*...*/} />
  <Text style={{ position: 'absolute', top: 0 }}>{text}</Text>
</View>

This could could probably be fixed by using RN 0.30.0 (see v0.30.0 release notes )

I tried it on RN 0.30 and on 0.31 RC, behavior doesn't change.

@yazgazan seems to be reasonable workaround

Still having this issue with RN 0.31 on Android

1. [Android] Container borderRadius covered by sub view #8649
2. overflow:hidden is not supported on Android #3198

Still having the same issue with RN 0.36 on Android.

Managed to solve the problem using the borderRadius attribute on the Image instead of providing as style.
RN 0.40

<Image
  source={{uri: 'http://lorempixel.com/400/300/'}}
  height={100}
  resizeMode="cover"
  borderRadius={10}
>
  <MyCustomComponent />
</Image>

Thanks @SushilShrestha for this. It works for me and has maybe saved me a couple of potentially agonizing minutes trying to find solutions. I have a Button element within my image which screwed up with its styling a bit, but adding borderRadius={50} to the Image and maintaining resizeMode: "cover" in my styles fixes the issue.

using RN 0.54.2 and issue still exists on android. so sad

Still happening & currently using @SushilShrestha 's fix

0.55 and still exists on android.

this fixes for me
<ImageBackground source={{ }} borderRadius={20}> <Text>Placeholder Text</Text> </ImageBackground>

resizeMode="cover" and borderRadius={n} got it to work on Android. Thanks for the tip, resizeMode is the key and also using borderRadius on the element itself.

Closing this since in #2468 there are multiple viable solutions.