The present article deals with the study of propagation of plane wave and fundamental solution in the thermoporoelastic medium. It is found that for two dimensional model, their exist three longitudinal waves, namely P1-wave, P2-wave and T-wave in addition to transverse wave. Characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and depicted graphically. The representation of the fundamental solution of the system of equations in the thermoporoelastic medium in case of steady oscillations is considered in term of elementary functions. Some basic properties of the fundamental solution are established. Some special cases are also deduced.