How to launch the external application in Delphi ?

You can launch application on windows by ShellExecute function. Following is the simple example to launch application.
 

use ShellAPI;

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ShellExecute(Handle, 'open', PChar('c:\estapp.exe'), nil, nil, SW_SHOW);

In case of running DOS command application such as batch file and you want not to display user, put SW_HIDE in the function option as follow
 

ShellExecute(Handle, 'open', PChar('c:\estkurapa_backup.bat'), nil, nil, SW_HIDE);