$re = '/\[\[File:[^[\]]*(?:\[\[[^[\]]*]][^[\]]*)*]]/';
$str = 'Some [[File:Edvac.jpg|thumb|[[EDVAC]], one of the first stored-program computers]] text';
$subst = "";
$result = preg_replace($re, $subst, $str);
echo "The result of the substitution is ".$result;
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for PHP, please visit: http://php.net/manual/en/ref.pcre.php