An unsteady two-dimensional MHD flow between the infinite parallel plates has been investigated. The effects of thermal radiation and magnetic field have been included in this model. The governing partial differential equations are transformed into the system of ordinary differential equations and then solved numerically by using Runge-Kutta based shooting technique. The impact of innumerable non-dimensional governing constraints on the velocity and temperature profiles along with the local Nusselt number, Squeeze number, Eckert number and the Prandtl number are analyzed in detail. The results indicate that the absolute skin friction coefficient increase with the increase in Squeeze number. It is also found that the Nusselt number is an increasing function of Squeeze number. © Research India Publications.