This article explores the micropolar fluid flow past a fluid sphere enclosing a solid core which is embedded in a porous medium. Flow fields of the porous region and nonporous region are governed by Brinkman equation and Stokes equation, respectively. Explicit expressions for stream functions, velocities, and microrotation components are examined. The drag force accomplished by a fluid sphere placed inside the porous medium is evaluated. The drag coefficient and its dependence are analyzed numerically and graphically with variation of permeability parameter and viscosity ratio. Some well-known results are validated with past known cases. © 2019 by Begell House, Inc.