Based on the microcosmic mechanics of composite materials, an elastic constitutive model for frozen soil with damage is presented. For frozen sandy soil with a range of ice contents and under a range of temperature conditions, quantitative results determined by this constitutive model agree with practically measured stress-strain curves. After numerically simulating the coupled water, temperature and stress fields of channel frozen and frozen roadbed using a self-developed finite-element routine, more accurate and practical calculation results for the temperature field coupled with stress, displacement and strain fields are obtained; the results match predictions and tests undertaken by earlier researchers. Our results support the reliability of our routine for calculating interdependent physical quantities of frozen soil and for describing the relationships between them. Our program can offer necessary constraints for engineering design and construction in permafrost regions. Based on the microcosmic mechanics of composite materials, an elastic constitutive model for frozen soil with damage is presented. For frozen sandy soil with a range of ice contents and under a range of temperature conditions, quantitative results determined by this constitutive model agree with practically measured stress-strain curves. After numerically simulating the coupled water, temperature and stress fields of channel frozen and frozen roadbed using a self-developed finite-element routine, more accurate and practical calculation results for the temperature field coupled with stress, displacement and strain fields the results match predictions and tests undertaken by earlier researchers. Our results support the reliability of our routine for calculating interdependent physical quantities of frozen soil and for describing the relationships between them. Our program can offer necessary constraints for engineering design and construction in permafrost regions.