The state space approach to generalized thermoelasticity is reformulated, and it is established that the solutions to the generalized thermoelastic fields can be formed by an entirely different approach as was illustrated by Sosa and Baharfor coupled thermoelastic problems. The article is concerned with a one-dimensional description of a semi-infinite body subjected to two types of boundary conditions; namely: (i)a step input of temperature and zero stress and(ii) a step input of stress and zero temperature. The various results obtained are found to be discontinuous for certain values of time in both the Lord and Shulman and the Green and Lindsay theories of thermoelasticity, and most of the jumps are shown to decay exponentially with time. The results for conventional coupled theory of thermoelasticity are obtained as a particular case of the generalized theory.