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In this article, the exact solution for a couple stress fluid flow past a fluid sphere filled with a couple stress fluid is considered using interfacial slip on the boundary. The velocity is expressed with regard to the stream function. The external velocity and internal velocity are alongside the drag coefficient. It was noticed that with the increases in slip parameter, the drag coefficient is decreasing and the inflow pattern has more circulations with more area appearing near the poles and internal flow disappears gradually. The special cases of viscous fluid, no-slip condition, and solid sphere are evaluated. A good understanding of the current and literature outcomes have been obtained, including the special case of a viscous fluid past a couple stress fluid sphere. [ABSTRACT FROM AUTHOR]