Based on the PM-PM-HS/ID model, the dynamic response of an isothermal three-phase catalytic reactor with a first order reaction in uniform spherical catalyst particles was presented analytically. The solution is valid for any mode of input perturbation with non-negative and constant initial conditions, and for continuous and semi-batch operations. Two critical Thiele moduli divide the solution into five cases and the dynamic response depends on the magnitude of the Thiele modulus. For the semi-batch operation with a sudden introduction of catalyst into the reactor, there exists two types of response for the effluent reactants in both gas and liquid phases, and the responses are distinguished by the first critical Thiele modulus. Based on the difference of the responses, a method which is able to determine the rate constant directly from the experiments was also proposed. For the continuous operation, two types of response always exist if the inlet liquid stream is pre-equilibrated with a gas which has the same composition as the inlet gas stream. The criterion to distinguish these two responses was also given. However, if there is no gas reactant dissolved in the inlet liquid stream, it is possible to have only the decay type response as the liquid flow rate is larger than some critical value.