try {
  //some code here for service call
}catch(SocketTimeoutException e)
{
  //not able to come here even though cause of the PrivilegedActionException is SocketTimeoutException
}
catch(Exception e)
{
  //directly coming here OF COURSE
}

java.security.PrivilegedActionException: com.sun.xml.internal.messaging.saaj.SOAPExceptionImpl: Message send failed
com.sun.xml.internal.messaging.saaj.SOAPExceptionImpl: java.security.PrivilegedActionException: com.sun.xml.internal.messaging.saaj.SOAPExceptionImpl: Message send failed

try{

}catch(PrivilegedActionException e){
    Throwable tmp = e;
    while(tmp != null){
        if(tmp instanceof SocketTimeoutException){
            SocketTimeoutException cause = (SocketTimeoutException) tmp;
            //Do what you need to do here.
            break;
        }
        tmp = tmp.getCause();
    }
}

catch(Exception e){
    if(e instanceof PrivilegedActionException){
         //while loop here
    }
}