Dynamical transport processes coupled to degradation in random mat- erials will be studied. In particular, we will concentrate on the two following problems: l)Fracture due to thermal shocks in brittle materials, and 2) stress-induced permeability changes in porous media during flow. The first problem arises in many practical situ- ations such as when pouring hot tea into a cold glas, or in any kind of industrial process where equipment is exposed to rapid temperature changes. The second problem concerns how an external deformation changes the flow field in a porous material, and how this change acts back on the stress field. This is a problem that for example is of concern to oil recovery in connection with load changes in the region near bore holes. Our approach is theoretical, and will be supported by extensive numerical modeling. It will form the basis for design of experi- ments to be conducted at the University of Oslo. Key words in connection with the theoretical analysis are self Organisation, criticality and scaling.