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The effects of thermal radiation and magnetic field on flow and heat transfer over an unsteady stretching surface in a micropolar fluid are studied. The governing partial differential equations are transformed into a system of ordinary differential equations containing the material parameter K, magnetic parameter M, radiation parameter R, and Prandtl number Pr. These equations are solved numerically by applying a shooting technique, using the Runge–Kutta method. Comparison of the numerical results is made with previously published results under the special cases, and the results are found to be in good agreement. Effects of the material parameter K, magnetic parameter M, radiation parameter R, and Prandtl number Pr on the flow and heat transfer are studied.