A dome-covered house is an example of designing sustainable buildings by learning from the optimized biological forms from the nature. This dissertation presents a three-dimensional thermal and air flow (3D-TAF) model that estimates the energy needs of a dome-covered house.  The mathematical model is composed of two components, that is, the thermal model and the air flow model, which are solved iteratively at every time step until the convergence is reached. The thermal model calculates the temperature of some nodes of interest of the simulation domain. The heat balance equations are written for: (a) the dome glazing; (b) the exterior envelope and the floor of the house; (c) the air inside the house; and (d) the earth surfaces inside the dome. The airflow model calculates the air velocities inside the dome, which are required by the thermal model to estimate the convective heat flow rate at the interface solid-air (e.g., between the dome cover and the dome air). It calculates also the vertical and horizontal temperature gradient of the air inside the dome.  Numerical method for solving the mathematical model is presented, which includes the discretization schemes, formation of the system of equations, initial values of the unknowns, solution algorithm and calculation procedure.  The validity of the mathematical model is demonstrated by comparison with a simplified computer model under MATLAB environment, with results from a 2D CFD model under the COMSOL Multiphysics environment, and with measured data and simulation results from similar structures, published by other researchers. The results have verified that the model gives good prediction on the temperature of the dome glazing, the air temperature and the air movement inside the dome.  A transparent dome, built above one house located in Montreal is selected as a case study. The simulation results predict a reduction of 62.6% of the annual heating load of a house when a dome is used, compared with the case of an unprotected house. Sensitivity analysis of the impact of optical properties of the dome glazing, natural infiltration/exfiltration through the dome/house, shape of the dome, and ground thermal properties on the heating load of the house is presented