The paper presents an integrated assessment model of an energy supply system for an energy-efficient building (ESSINTEGRA). This assessment comprises a comprehensive analysis of the building energy demand and energy supply systems as well as determining a rational solution on the basis of the selected assessment criteria: energy efficiency, environmental impact, economic, comfort and technical functionality. ESSINTEGRA is applied for a case study of a single family house. Six different alternatives of the house envelope parameters and 15 combinations of the technological solutions of the building energy supply systems (BESS) are explored as design options. Applying the model has allowed to determine the rational solution for the energy-efficient single family houses in Northern European climate (zone 5). When the combination of the wood boiler with a solar collector system is used, the primary energy demand of 10.1 kWh/m(2), CO2 gas emissions of 0.24 kgCO(2)/m(2) and the renewable energy fraction of 97.4 % can be obtained. When the decision making method is applied, the reliability of the rational solution amounts to 99.5%. The sensitivity analysis has shown that the variation of the criteria significances has no influence on the reliability of the rational solution. (C) 2016 Elsevier B.V. All rights reserved.