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A numerical analysis of an unsteady radiative and viscous dissipative fluid flow across a semi-infinite oscillating vertical plate with a constant temperature and mass diffusion is examined here. The fluid under consideration is optically thin gray, emitting, heat-retaining, and non-dispersing. A finite-difference approach known as the Crank−Nicolson strategy was applied to find the solution to the limitless governing equations. Applications of such engineering problems can be found in fields such as aerospace, solar power, the cooling of nuclear reactors, and chemical and mechanical engineering. Based on the computational solutions, the impacts of distinct physical parameters, such as velocity, concentration, temperature, skin friction, Nusselt number, and Sherwood number profiles, are portrayed pictorially and imparted. The numerical solution of the velocity profile developed in this study fits extremely well with what was previously published and validated. Furthermore, we discovered that plate oscillation, radiation, and viscous dissipation parameters surprisingly influence the flow pattern.