Abstract—The issues of the mathematical modeling of a thermoporoelastic medium taking its damage into account are considered. The employed model generalizes the classical Biot model simulating the behavior of a poroelastic medium taking the thermoelastic effects into account. In order to describe the damage of the medium, the approach of continual damage mechanics is used, in which the state of the medium is described by the scalar damage parameter, which affects the elastic and poroperm characteristics of the medium. The system of the governing equations for the model consists of the fundamental mass, momentum, and energy conservation laws and is closed by thermodynamically consistent constitutive relations. Moreover, the medium’s energy expression takes into account its changes due to the formation of damaged zones. The computational algorithm is based on the finite-element method. A monolithic approach is used, which assumes that all groups of equations (mechanics, heat transfer, and flow) are solved simultaneously without being split into physical processes and/or iterations between groups of equations. The system of equations of thermoporoelasticity is approximated by a fully implicit scheme. The damage parameter’s evolution depending on the stress-strain state of the medium can be described in terms of both instant and finite-time kinetics. This paper briefly describes the mathematical model and presents a detailed description of the computational algorithm and its implementation. A significant part of the study is devoted to the application of the developed approaches for solving several model and realistic three-dimensional problems. The analysis of the geomechanical problems of thermal enhanced oil recovery methods, which require a consistent description of the elastic, filtration, and thermal fields’ dynamics taking into account the evolution of the medium’s fracture, is considered to be the main field of the application of the model and algorithm.