An analytical solution for the frequency response of a semi-batch adsorption vessel with sinusoidal modulation of molar flow rate, loaded with inert core adsorbents is obtained for a linear isotherm coupled with intraparticle diffusion and external film diffusion. The low-frequency limiting values of the in-phase and the out-of-phase characteristic functions of the frequency response are found to be explicit functions of the size of the inert core and the external mass transfer parameter. Simulation results of the in-phase and the out-of-phase characteristic functions show that there exist a crossover frequency and overshoot of the in-phase characteristic function when external mass transfer resistance is present.