Flutterの公式ドキュメントにNavigate with named routesというサンプルがありますが、こちらの書き方でページ遷移を実装すると、簡潔に書くことができます。

しかし、文字列をそのまま与えてしまうと、typo等で間違ってしまうことがあるので、以下のようなクラスを作ってあげることでそれを解決します。

class RouteNames {
  static const String first = '/';
  static const String second = '/second';
}

Navigator.push(context, RouteNames.second);

Before

import 'package:flutter/material.dart';

void main() {
  runApp(MaterialApp(
    title: 'Named Routes Demo',
    initialRoute: '/',
    routes: {
      '/': (context) => FirstScreen(),
      '/second': (context) => SecondScreen(),
    },
  ));
}

class FirstScreen extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text('First Screen'),
      ),
      body: Center(
        child: RaisedButton(
          child: Text('Launch screen'),
          onPressed: () {
            Navigator.pushNamed(context, '/second');
          },
        ),
      ),
    );
  }
}

class SecondScreen extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text("Second Screen"),
      ),
      body: Center(
        child: RaisedButton(
          onPressed: () {
            Navigator.pop(context);
          },
          child: Text('Go back!'),
        ),
      ),
    );
  }
}

After

import 'package:flutter/material.dart';

void main() {
  runApp(MaterialApp(
    title: 'Named Routes Demo',
    initialRoute: '/',
    routes: {
      RouteNames.first: (context) => FirstScreen(),
      RouteNames.second: (context) => SecondScreen(),
    },
  ));
}

class RouteNames {
  static const String first = '/';
  static const String second = '/second';
}

class FirstScreen extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text('First Screen'),
      ),
      body: Center(
        child: RaisedButton(
          child: Text('Launch screen'),
          onPressed: () {
            Navigator.pushNamed(context, RouteNames.second);
          },
        ),
      ),
    );
  }
}

class SecondScreen extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text("Second Screen"),
      ),
      body: Center(
        child: RaisedButton(
          onPressed: () {
            Navigator.pop(context);
          },
          child: Text('Go back!'),
        ),
      ),
    );
  }
}