This is a survey article on the modeling of thermoelastic waves in a solid
body. The term "Generalized Thermoelasticity" stands for a Hyperbolic Therm
oelasticity in which a thermomechanical load applied to a body is transmitt
ed in a wave-like manner throughout the body. Only transient thermoelastic
waves are included in the survey. The modeling covers: (i) L-S model (Lord
and Shulman, 1967), (ii) G-L model (Green and Lindsay, 1972), (iii) H-I mod
el (Hetnarski and Ignaczak, 1996), (iv) G-N model (Green and Naghdi, 1993),
and (v) C-T model (Chandrasekharaiah and Tzou, 1998). Attention focuses on
the theoretical and practical significance of these models. Theoretical re
sults include the domain of influence theorems, uniqueness as well as one-d
imensional closed-form solutions. Except for a limiting case when the model
s reduce to rigid heat conductors, none of the five models has been verifie
d by a combined thermoelastic experiment up to date, so their applications
to real thermoelastic bodies present a challenge for future generations of
researchers in the field.