The two-dimensional slow viscous fluid motion between two co-axial circular cylinders showed the inner cylinder is shear-free and the outer one is rigid. The flow is due to the presence of a line source and a line sink of equal strength on the outer cylinder. The stream function for the flow in the annular region is established. The hydrodynamic force on the inner shear-free cylinder has been evaluated. Some numerical values for the force have been presented in a table and compared with corresponding known values where both inner and outer cylinders are rigid. DOI: http://dx.doi.org/10.3329/jbas.v36i1.10928 Journal of Bangladesh Academy of Sciences, Vol. 36, No. 1, 123-135, 2012
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