The paper deals with modelling the process both of peak catastrophic emissions of contaminated liquids or wastewater during dams break and describing the spread of pollution caused by these incidents in adjacent reservoirs. In the first part of the paper the methods and algorithms for numerical solution of problems of water filtration through broken dams. The novelty of this part is that models and algorithms for calculating pollutions in ground materials both with isotropic and with orthotropic properties have been developed. In the next part of the paper the simple model describing the relaxation impact of the pollutions in the system of interconnecting water reservoirs after wastewater emissions through the broken dams has been submitted. The appropriate code and soft for the numerical experiments at different pollution discharge durations and various relations of the filtration coefficients have been developed and tested. The pollution relaxation times in the system of water reservoirs have been studied.