This paper deals with the dynamic treatment of a transient thermoelastic problem for an elastic half‐space that is exposed to step temperature and velocity on its entire plane boundary and is constrained against transverse displacements. The stress distribution pertaining to this problem, whose plane boundary is subjected to step‐ and/or ramp‐type temperature only, was previously treated by V. I. Danilovskaya [Prikl. Mat. i Mekhan.14, 316–318 (1950)], T. Mura [Proc. Japan Natl. Congr. Appl. Mech., 2nd, pp. 9–13 (1952)], and E. Sternberg and J. G. Chakravorty [J. Appl. Mech.26, 503–509 (1959)]. In physical reality, when the boundary experiences temperature variations, it often also experiences velocity variations. A comparison of present results with previous results reveals that the stress distributions are changed considerably once the velocity variation on the boundary is considered.