In the Czech Republic, double porosity soils exhibiting large total porosity are abundant in the clayfills of open-pit coal mines. Numerical analyses of such soils require unconventional procedures. The paper presents an approach to the constitutive modelling of double porosity materials. Application of the framework is demonstrated by an enhancement of the Modified Cam clay model. The results of laboratory experiments that have been carried out in the triaxial apparatus are used in calibrating the reference MCC model. The performance of the enhanced model is demonstrated by a parametric study.