how to run two queries using the code snippet below?

Create a Stored Procedure that updates the two tables and execute it using a StoredProcedure Command...

command.CommandType = CommandType.StoredProcedure;
command.CommandText = "UpdateTheTwoTables";
....

Modify the SQL statement to update the two tables.

Using a Stored Procedure is the cleanest way code wise. If you don't feel comfortable doing it like that, I'm sure you can do it like this:

Try
    Using conn = New SqlConnection(constr)
        Using cmd = conn.CreateCommand()
            conn.Open()
            Dim sql As String = "UPDATE a1_ticket SET Ticket_no =@ticketNo, BANK = @bank, PAID = @paid, BID = @bid WHERE ITC = @ticketNo"
            cmd.CommandText = sql
            cmd.Parameters.AddWithValue("@bank", Literal20.Text)
            cmd.Parameters.AddWithValue("@paid", Label1.Text)
            cmd.Parameters.AddWithValue("@bid", Literal21.Text)
            cmd.Parameters.AddWithValue("@ticketNo", Literal3.Text)
            cmd.ExecuteNonQuery()
        End Using
//
        Using cmd = conn.CreateCommand()
            conn.Open()
            Dim sql As String = "UPDATE a2_ticket SET Ticket_no =@ticketNo, BANK = @bank, PAID = @paid, BID = @bid WHERE ITC = @ticketNo"
            cmd.CommandText = sql
            cmd.Parameters.AddWithValue("@bank", Literal20.Text)
            cmd.Parameters.AddWithValue("@paid", Label1.Text)
            cmd.Parameters.AddWithValue("@bid", Literal21.Text)
            cmd.Parameters.AddWithValue("@ticketNo", Literal3.Text)
            cmd.ExecuteNonQuery()
        End Using
    End Using
Catch ex As Exception
    Response.Write(ex.Message)
End Try

It's a sketch of what I'm trying to say, you may want to change a few things here and there, but the point is you can just update your two tables one after the other. It's not possible in one update statement afaik.

you can also use

Dim sql As String = @ "Query for first update;

                       Query for second update;";   

Well as you havent said anything about the second table, or the data you're sending it. I havent put this through the compiler to verify it, but the concept I'd suggest would be

You could do:

void UpdateDB(String sql, String[][] params)
{
Try
{
    SqlConnection conn = New SqlConnection(constr);
        SqlCommand cmd = conn.CreateCommand();
            conn.Open();
            cmd.CommandText = sql;
            for(int i=0; i<params.length; i++)
            {
                cmd.Parameters.AddWithValue(params[i,0] params[i,1]);
            }
            cmd.ExecuteNonQuery();
}
Catch (Exception ex)
{
    Response.Write(ex.Message);
}
}

eg send the SQL and the parameters to the function and have it do all the work..