The transient boundary-layer evolution of an elastico-viscous medium along a persistently deforming sheet undergoing a first-order chemical reaction is investigated. The rheological behaviour of the elastico-viscous fluid is characterised through Walters’ liquid model (B′ formulation). By invoking similarity transformations, the controlling partial differential equations are recast into a coupled system of nonlinear self-similar ordinary differential equations subject to pertinent boundary constraints. These nonlinear relations are subsequently reduced to a set of first-order differential equations accompanied by their associated boundary specifications. The resulting system is tackled numerically via MATLAB’s intrinsic boundary-value solver bvp4c. The numerical solutions thus obtained are employed to construct velocity and concentration distributions for varying magnitudes of the governing parameters. Critical examination of the generated profiles demonstrates that both the hydrodynamic field and mass transport phenomena are profoundly modulated by the influence of the controlling flow parameters.