The design-application of thermal mass is a powerful tool for controlling temperature in buildings. Although a large volume of literature on the use of thermal masses in building applications exists, little quantitative characterization of the performance of a thermal mass under dynamic heating and cooling can be found. In this thesis, the performance of planar thermal masses (PTMs) subject to sinusoidal heating and cooling is investigated. Based on the analysis of a semi-infinite PTM under a sinusoidal thermal wave, some new definitions -- penetration depth, effective thickness, effective area specific heat and effective heat exchange coefficient are introduced. Since actual PTMs are not semi-infinite, the dynamic heat transfer process of finite-thickness PTMs -- one surface is under a sinusoidal thermal wave and the other one is specified with three kinds of boundary conditions-- are discussed. When inside air temperature is equal to the mean value of the outside surface temperature, analytical solutions of the temperature distribution and heat flux in finite-thickness PTMs are deduced. The effective heat exchange coefficient and, a new definition, the effective heat storage coefficient of PTMs with different thermo-physical properties are developed. For PTMs with the boundary condition of the second kind, an optimal effective thermal mass coefficient at an optimal thermal mass thickness is found. Because of the large effective area specific heat difference, wood is much worse than concrete for heat storage. When the inside air temperature is not equal to the mean value of the outside surface temperature, analytical solutions do not exist and numerical method is used to solve the dynamic heat transfer problem. Three forms of approximated temperature distribution are developed based on numerical calculations. The best one of the approximated forms is used to investigate the heat exchange between finite-thickness PTMs and the environment. From the approximated form, time lag and decrement factor are also obtained. Last, the comparison of wood and concrete, as exterior wall material, shows that wood is a better than concrete due to its lower conductivity.