A three-dimensional transient thermoelastic solution is obtained for Rayleigh-type disturbances propagating on the surface of a half-space. These surface waves are generated by either a buried or surface thermal source, which has the form of a concentrated heat flux applied impulsively. In an effort to model this problem as realistically as possible, the half-space material is taken to respond according to Biot’s fully coupled thermoelasticity. The problem has relevance to situations involving heat generation due to: (i) laser action (impulsive electromagnetic radiation) on a surface target, (ii) underground nuclear activity, and (iii) friction developed during underground fault motions related to seismic activity. The problem was attacked with unilateral and double bilateral Laplace transforms, which suppress, respectively, the time variable and two of the space variables. The Rayleigh wave contribution is obtained as a closed-form expression by utilizing asymptotics, complex-variable theory and certain results for Bessel functions. The dependence of the normal displacement associated with the Rayleigh wave upon the distance from the source epicenter and the distance from the wavefront is also determined.

*An Introduction to the Theory of Seismology*, Cambridge University Press, Cambridge.

*Wave Propagation in Elastic Solids*, North–Holland, NY.

*Thermomechanical Couplings in Solids*, edited by Bui, H. D. and Nguyen, Q. S., Elsevier, Amsterdam, pp. 305–318.

*Boundary Element Methods in Mechanics*, edited by Beskos, D. E., Elsevier, Amsterdam, pp. 440–498.

*Progress in Solid Mechanics*, edited by Sneddon, I. N. and Hill, R., North–Holland, Amsterdam, Vol. 1, pp. 263–328.

*Handbuch der Physik*, edited by Flugge, S., Springer-Verlag, Berlin,

**VIa/2**, pp. 297–345.

*The Theory of Elastic Waves and Waveguides*, North–Holland, Amsterdam.

*Operational Calculus Based on the Two-Sided Laplace Integral*, Cambridge University Press, Cambridge.

*Functions of a Complex Variable*, McGraw–Hill, New York.

*Rayleigh and Lamb Waves*, Plenum Press, NY.

*Complex Variables*, Cambridge University Press, Cambridge.

*Theory of Bessel Functions*, Cambridge University Press, Cambridge.

*The Fourier Transform and Its Applications*, McGraw–Hill, New York.