A rigid constitution is one which cannot be amended, in the manner in which ordinary laws are passed amended or repealed. If a special procedure or organ is needed for its amendment, it is a rigid constitution.
As Gettle says, "Its laws are thus fixed and emanate from a source different from that of ordinary laws, which must keep within the bounds fixed by the constitution". A law which the constitution forbids or a law made by an organ not empowered to do so by the constitution shall be an unconstitutional law.
Ordinary legislature of the country is not competent to amend it in the ordinary legislative procedure. Under a rigid constitution distinction is always maintained between a constitutional law and an ordinary law, since a constitutional law is regarded as superior to an ordinary law.
Constitutional law cannot be amended by the ordinary legislature using normal legislative procedure. Moreover, a rigid constitution is the supreme law of the land and ordinary legislature cannot pass a law which is repugnant to its spirit. The legislature under a rigid constitution is not sovereign. Its authority is limited by the constitution.
The American constitution is a classical example of rigid constitution. It cannot be amended in the manner in which ordinary laws are passed, amended or repealed. A distinction is maintained between a constitutional and an ordinary law. Both are not placed on an equal footing.
There is a special procedure for constitutional amendment. Ordinary law in U.S.A. can be passed by a simple majority of the Congress, whereas the constitutional laws can be amended only by the agreement of two thirds majority of the Congress and three fourths of the states.
The Swiss constitution is still more rigid. An amendment whether proposed by the Federal Assembly or through initiative needs to be approved by the Cantons and the electorate through referendum. It must be, thus approved by majority of all the voters casting their vote and by majority of such votes in majority of Cantons.
A flexible constitution is one which can be amended in an ordinary legislative process by the ordinary legislature. A Constitutional law and an ordinary law are treated alike.
They are placed on an equal footing. All constitutional amendments can be made by a simple majority of the legislature. No distinction is made between the constitution making authority and the ordinary law making authority.
No law is unconstitutional if passed by the Parliament. It is a sovereign body, at once enjoying the ordinary law making powers and constitutional law making powers. It is at once a legislature and a constituent assembly.
The constitution of England is a typical example of a flexible constitution. The British Parliament is competent to pass, amend or repeal any constitutional law in an ordinary legislative process as both constitutional laws and ordinary laws are treated alike.