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In this paper, the flow generated by the slow steady rotation of a permeable sphere with thin surface about its axis of symmetry in an incompressible couple stress fluid which is otherwise at rest is studied. Expressions for the velocity and couple stress tensor components are obtained in terms of modified Bessel functions and Gagenbauer’s polynomials. The couple experienced by the permeable sphere due to the internal and external flow is evaluated. The more is couple stress offered by the fluid (i.e. the lesser values of couple stress parameter), the more the fluid particles are thrown away from the sphere. It is noticed that the internal flow is similar to viscous flow and the couple acting on the sphere due to internal flow is zero. The problem differs from that of micro-polar fluids. Keywords: Permeable sphere, Couple stress fluid, Rotary flow, Modified Bessel functions, Gagenbauer functions