We report a method for calculating the response time of a hollow fibre supported liquid membrane (SLM) for metal preconcentration. The SLM system is composed of three distinct compartments : an internal stripping solution (filling the hollow fibre lumen), a hydrophobic liquid membrane (adsorbed in the hollow fibre pores), and an external source solution (containing the analyte). The calculation consists of resolving the diffusion equation which describes the evolution of the concentration of the metal ion in the system. The Laplace transform method is used for this purpose, and the inverse Laplace transformation is performed using discrete Fourier transforms. Variation in the concentration of the strip solution with time, after a given change in concentration of the source solution, can be predicted from these calculations. The numerical results obtained by considering various geometrical (membrane thickness, lumen diameter), hydrodynamic (Nernst layer thickness) and chemical (diffusion and partitioning constants) conditions, are presented in order to allow optimization of the system, i.e. reproducibility, fast response time, and high metal preconcentration.