  This paper is concerned with the linear theory of thermoelasticity with
microtemperatures, based on the entropy balance proposed by Green and Naghdi,
which permits the transmission of heat as thermal waves of finite speed. We
analyze the behavior of Rayleigh waves in an unbounded isotropic homogeneous
strongly elliptic thermoelastic material with microtemperatures. The related
solution of the Rayleigh surface wave problem is expressed as a linear
combination of the elements of the bases of the kernels of appropriate
matrices. The secular equation is established and afterwards an explicit form
is written when some coupling constitutive coefficients vanish. Then, we solve
numerically the secular equation by mean of a grafical metod and by taking
arbitrary data for strongly elliptic thermoelastic material.
