Of interest here are dynamic thermoelastic problems influenced by second sound effects. In this regard, the effect of the so called 'heat waves' on solid continua is investigated employing a 'unified' explicit computational architecture which uses the finite element method. The approach is robust and effective for transient interdisciplinary thermal-structural modeling/analysis. The non-classical relaxation model of Green and Lindsay (1972) involving two relaxation times is employed in the present work. Numerical simulations relevant to thermal shock problems in an elastic half-space are described for stainless steel via two different illustrative test cases.