The thermoelasticity of an anisotropic Hookean half space is studied herein. A solution based on successive integral transforms is developed. The solution can handle arbitrary thermal and mechanical boundary conditions together with distributed body forces and heat sinks or sources. To illustrate the substantial effects of material anisotropy, a specific boundary-value problem is solved. Numerical results based on the solution are presented. These illustrate the significant effects of both thermal and mechanical material anisotropy.

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