Membrane processes utilizing hollow fibre membrane modules are gaining increased interest in many industrial applications. However, these modules suffer from shell-side maldistribution and bypassing which results in a loss in efficiency. The shell-side mass transfer performance of these membrane modules strongly depends on the shell-side mixing and the shell geometry. In literature limited information is available on the shell-side mixing of hollow fibre membrane modules. In the present work, shell-side mixing of a rectangular cross-flow hollow fibre membrane contactor is investigated using gas-phase RTD measurements. A novel ultrasound based measurement technique was used to characterize the system. The shell-side mixing of the module is determined in terms of dispersion coefficients in three directions. The axial dispersion coefficient is found to have values between those applicable to pipe-flow and packed bed correlations. This can be attributed to the intermediate packing density of the membrane module. The dispersion in transversal directions, along and across the fibres, is significantly lower compared to that of the axial dispersion. The transversal dispersion coefficient across the fibre is higher and more sensitive to the shell-side velocity compared to the dispersion coefficient along the fibre due to the continuous splitting and remixing of shell-side flow across the fibres.