<p>We describe via semigroup techniques the space decaying solutions to the system modeling an isotropic and homogeneous elastostatic semi-infinite band, both in the isothermal case and when thermal effects are present. The semigroup approach allows us to transfer some properties that typically occur in evolution problems to our model, such as analyticity and exponential decay at infinity. These results are closely related to the Saint-Venant principle. We conclude the article by recalling some consequences of the analyticity of the semigroup. The resulting properties are rather innovative compared to the usual results in the literature concerning the spatial decay of solutions.</p>