Fine finishing of cylindrical internal surfaces without affecting geometric form is a critical requirement in several mechanical and aerospace applications. Although various methodologies using flexible abrasive media are reported for the same, many of them demands complex tooling and fixtures to be developed in tune with the internal dimensions to feed the abrasive media. Present paper investigates the feasibility of using magneto-elastic abrasive balls with the aid of a mechanically deployable tool for micro-finishing of geometrically symmetric tubular specimens. The deployable tool used for the present experimentation is designed like an umbrella mechanism, with magnetic pads to hold the elastic abrasive balls, expandable for bore diameter ranges from 45 to 75 mm. The magnetic type elastic abrasive balls proposed in the form of meso-scale balls of diameter 3.5 ± 0.25 mm are capable of finishing the bore surface without altering its roundness. Effects of elastomeric medium, mechanics of material removal and generation of finished profile during the proposed technique have been discussed in detail, through a comprehensive mathematical model. Effect of various process variables on surface roughness was investigated experimentally using response surface methodology and the theoretical predictions were validated at optimum operating condition. 62% reduction in average roughness on brass tubes of initial roughness 0.168µm, with significant improvement in all the associated 2D roughness parameters and without any deviation on roundness, was clearly demonstrating the potential of proposed methodology.