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In the present study, Unsteady Oscillatory Couette Flow between vertical parallel plates with constant radiative heat flux is considered. The mathematically formulated governing equations are simplified with dimensionless variables and coupled ordinary differential equations were obtained. Rosseland approximation is used and the present study is therefore for a case of to an optically thick fluid like blood. The transformed set of coupled nonlinear ordinary differential equations is then solved analytically using the perturbation method, and the velocity and temperature functions are simulated. It is observed that increasing the thermal radiation parameter Rd increases the blood flow, in addition, the oscillatory frequency ω also improves the flow profiles such as temperature θ(y) and velocity w(y).