A Visual Studio sollution prepared to be used (plug and play) with Docker. It will create 2 contaners, one for the web server and one for the SQL server (both running on Linux).

To whole tutorial about creating this solution is available in my blog post .NET Core Web App Docker and MSSQL Docker

Code: A code example of a SQL connection (MSSQL is located in another container) is located in the following file: Controllers/HomeController.cs. The important lines are:

//CONNECTION STRING TEST - BEGIN
/*
SqlConnection cnn;
var connection = @"Server=db;Database=dean;User=sa;Password=TestPassZXY017+;";
cnn = new SqlConnection(connection);
try
{
    cnn.Open();
    cnn.Close();
}
catch (Exception ex)
{

}
//*/
//CONNECTION STRING TEST - END

Server=db: "db" is the name of the image instance (container), which is defined in the docker-compose.yml file below.

All the mentioned lines above are commented out, bacause at the first project run you need to create a DB first (used DB name in this example is 'dean'). When you will create a DB, uncomment those lines and at the next application start, the C# code above should establish a connection to the MS SQL server without any errors.

version: '3'

services:
  webapplication1:
    image: webapplication1
    build:
      context: ./WebApplication1
      dockerfile: Dockerfile
  db:
    image: "microsoft/mssql-server-linux"
    environment:
      SA_PASSWORD: "ZacetnoGeslo2017+"
      ACCEPT_EULA: "Y"
    ports:
    - "1433:1433"

webapplication1 is a container for the Web Server

db is a container for hodling the MS SQL Server