I use
Hibernate 3.2.1 ga,
c3p0-0.9.0.jar (which is distributed along with hibernate),
jdk 1.4.2,
Oracle 10g XE database.

using the following code

SessionFactory sessionFactory = new Configuration().configure().buildSessionFactory();

session = sessionFactory.getCurrentSession();

Transaction tx = session.beginTransaction();
:::
:::
:::
:::

tx.commit();
session.flush();
session.close();

Exception in thread "main" org.hibernate.SessionException: Session was already closed at session.flush() line

When we comit a transaction hibernate by default flushes the session implicitly. So there is no need to explicitly call it. Hope that helps.

I commented out the session.flush() and then tried it again.

Again the same error at session.close() line.

So if we commit the transaction, will session.flush() & session.close() happen automatically?

Sorry for not being explicit.

Yes, you really dont need both flush and close.
Commit or rollback does those two operations implicitly.

So if after commit/rollback if you need to open a new transaction then you need to create (or get) a new session from the sessionfactory.

Hope that helps.