Scale free graphs have attracted attention
by their non-uniform structure that can be used as a model
for various social and physical networks.
In this paper, we propose
two natural and simple random models
for generating scale free interval graphs.
These models generate a set of intervals randomly,
which defines a random interval graph.
The main advantage of those models are its simpleness.
The structure/properties of the generated graphs are analyzable
by relatively simple probabilistic and/or combinatorial arguments,
which is different from the most of the other models
for which we need to approximate the processes
by certain differential equations.
We indeed show that the distribution of degrees follows power law,
and  it achieves large cluster coefficient.