We introduce a computer implementation of the mathematical model of capillary zone electrophoresis described in the previous paper in this issue (Hruska et al., Electrophoresis 2012, 33), the program PeakMaster 5.3. The computer model calculates eigenmobilities, which are the eigenvalues of the Jacobian matrix of the electromigration system, and which are responsible for the presence of system eigenzones (system zones, system peaks). The model also calculates parameters of the background electrolyte: pH, conductivity, buffer capacity, ionic strength, etc., and parameters of the separated analytes: effective mobility, transfer ratio, molar conductivity detection response, and relative velocity slope. In addition to what was possible in the previous versions of PeakMaster, Version 5.3 can predict the shapes of the system peaks even for a complex injected sample profile, such as a rectangular plug. PeakMaster 5.3 can replace numerical simulation in many practically important configurations and the results are obtained in a very short time (within seconds). We demonstrate that the results obtained in real experiments agree well with those calculated by PeakMaster 5.3.