How can we say that our Constitution is partly rigid and partly flexible?

It is a blend of rigidity and flexibility.

As provisions of the Constitution could be amended but there are also conditions like there must be a special majority to amend the Constitution.

Article 368 in Part XX of the Constitution deals with the powers of Parliament to amend the Constitution and its procedure. It states that the parliament may incorporate changes to the Constitution when required but without changing the basic structure of the Constitution.

1. An amendment of the Constitution can be initiated only by the introduction of a bill for the purpose in either House of Parliament

2. The bill must be passed in each House by a special majority

3. After duly passed by both the Houses of Parliament and ratified by the state legislatures, where necessary, the bill is presented to the President for assent.

After the President’s assent, the bill becomes an Act.