A stress-affected chemical reaction front propagation is considered using the concept of a chemical affinity tensor. A reaction between an elastic solid constituent and a diffusing constituent, localized at the reaction front, is considered. As a result of the reaction, the elastic constituent transforms into viscoelastic one. The reaction is accompanied by volume expansion that in turn may result in stresses at the reaction front, which affect the front velocity through the normal component of the chemical affinity tensor. Considering a plane strain problem with a planar chemical reaction front propagation under uniaxial deformation, we focus on the studies of the reaction front kinetics in dependence on external strains and material parameters with the use of the notion of the equilibrium concentration. Then, stress relaxation behind the propagating reaction front is modeled. A standard linear solid model is used for the reaction product, and its particular cases are also considered. Analytical solutions are obtained which allow to study in explicit form the strain influence and material parameters on the front retardation or acceleration and stress relaxation.