In this work several problems related to thermal spalling are considered. First, a novel approximate technique to solve general linear heat-conduction problems with changing boundary conditions and locations is proposed. The technique is based on the concept of linear superposition and the possibility to transform the initial condition into a time-varying boundary condition. The proposed technique is evaluated and compared_to some of the existing techniques. The individual contribution of several stress components and their combined effects on the risk of failure are then considered for a theoretical axi-symmetric body subjected to uniform unconfined heating. The results indicate that using a single stress component in the prediction of failure for brittle materials is not justified in general. Finally, the thermal spalling process in jet piercing operations is studied. The finite element model consists of a large axi-symmetric object subjected to a confined heat flux. The numerical results are used to study the combined effects of several stress components and the influence of material properties and heat flux intensity on the spalling rate and spallability of brittle materials. The results compare favorably with experimental results reported in the literature. A set of plots are offered for use in design. Possible extensions and variations of the present work are also discussed. / Ph. D.