  Higgs cubic coupling plays a crucial role to probe an origin of electroweak
symmetry breaking. It is expected that the cubic coupling is measured by Higgs
pair production at the LHC and ILC, and the deviations from the standard model
can be extracted from the Higgs pair production process, and those can give us
a hint of new physics beyond the standard model. We consider a general
potential that achieves the suitable electroweak symmetry breaking. As one of
the interesting models, we suggest a non-perturbative Higgs model in which a
run-away type of potential is used. In the model, the cross sections of pair
production at the LHC is enlarged compared to the standard model. We also study
the Higgs pair production induced by a non-canonical kinetic term of Higgs
fields which will be important to search the pair-production at the ILC.
