In this paper, multiple front phase change problems in one-dimensional cylindrical systems are investigated. The objective is to develop a numerical solution using the BEM for freezing and melting problems involving multiple moving fronts. Multiple moving phase fronts arise when the phase change material (PCM) is subjected to alternate driving temperatures that cause the surface temperature of the PCM to change back and forth across the phase change temperature. This kind of problem is highly nonlinear at the phase fronts that separate alternate liquid and solid layers with different properties.Fully implicit time discretization is applied to ensure numerically stable results. Numerical results are presented for a cylindrical problem with the inner surface subjected to a convective environment where the temperature changes between values above and below the freeze temperature of the PCM. This condition could occur in ice thermal storage systems. The numerical behavior of the creation and collapse of the moving fronts is investigated by changing the Stefan number, Biot number, initial temperature, the cycling time length and the time step size.