Horizontally scrollable cards with Snap effect in flutter

Use PageView and ListView:

import 'package:flutter/material.dart';

main() => runApp(MaterialApp(home: MyHomePage()));

class MyHomePage extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text('Carousel in vertical scrollable'),
      ),
      body: ListView.builder(
        padding: EdgeInsets.symmetric(vertical: 16.0),
        itemBuilder: (BuildContext context, int index) {
          if(index % 2 == 0) {
            return _buildCarousel(context, index ~/ 2);
          }
          else {
            return Divider();
          }
        },
      ),
    );
  }

  Widget _buildCarousel(BuildContext context, int carouselIndex) {
    return Column(
      mainAxisSize: MainAxisSize.min,
      children: <Widget>[
        Text('Carousel $carouselIndex'),
        SizedBox(
          // you may want to use an aspect ratio here for tablet support
          height: 200.0,
          child: PageView.builder(
            // store this controller in a State to save the carousel scroll position
            controller: PageController(viewportFraction: 0.8),
            itemBuilder: (BuildContext context, int itemIndex) {
              return _buildCarouselItem(context, carouselIndex, itemIndex);
            },
          ),
        )
      ],
    );
  }

  Widget _buildCarouselItem(BuildContext context, int carouselIndex, int itemIndex) {
    return Padding(
      padding: EdgeInsets.symmetric(horizontal: 4.0),
      child: Container(
        decoration: BoxDecoration(
          color: Colors.grey,
          borderRadius: BorderRadius.all(Radius.circular(4.0)),
        ),
      ),
    );
  }
}

Screenshot:

If you don't want to use any 3rd party packages, you can simply try this:

class _HomePageState extends State<HomePage> {
  int _index = 0;

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(),
      body: Center(
        child: SizedBox(
          height: 200, // card height
          child: PageView.builder(
            itemCount: 10,
            controller: PageController(viewportFraction: 0.7),
            onPageChanged: (int index) => setState(() => _index = index),
            itemBuilder: (_, i) {
              return Transform.scale(
                scale: i == _index ? 1 : 0.9,
                child: Card(
                  elevation: 6,
                  shape: RoundedRectangleBorder(borderRadius: BorderRadius.circular(20)),
                  child: Center(
                    child: Text(
                      "Card ${i + 1}",
                      style: TextStyle(fontSize: 32),
                    ),
                  ),
                ),
              );
            },
          ),
        ),
      ),
    );
  }
}

this is an old question, and I arrived here looking for something else ;-), but what WitVault was lookig is done easy with this package: https://pub.dev/packages/flutter_swiper

The implementation:

Put the dependencies in pubsec.yaml:

dependencies:
   flutter_swiper: ^1.1.6

Import it in the page where you need it:

import 'package:flutter_swiper/flutter_swiper.dart';

In the layout:

new Swiper(
  itemBuilder: (BuildContext context, int index) {
    return new Image.network(
      "http://via.placeholder.com/288x188",
      fit: BoxFit.fill,
    );
  },
  itemCount: 10,
  viewportFraction: 0.8,
  scale: 0.9,
)

To achieve the snap effect via ListView, just set the physics to PageScrollPhysics

const List<Widget> children = [
  ContainerCard(),
  ContainerCard(),
  ContainerCard(),
];
ListView.builder(
    scrollDirection: Axis.horizontal,
    physics: const PageScrollPhysics(), // this for snapping
    itemCount: children.length,
    itemBuilder: (_, index) => children[index],
  )