In this paper we discuss some problems of modeling of beam slow extraction systems. It is known that similar type of beam extraction is used for different kind of circular accelerators. Among the most important requirements for such systems is necessary to mention the time uniformity of the extracted beam. There exist the following two key causes. The first of them is induced by time discontinuity of the corresponding steering electrical currents, and the second cause is induced by an beam inertia which usually connected with beam feedback mechanism, which is usually used for temporal smoothing of the corresponding magnetic (and electrical) fields. In the base of our approach we put the matrix formalism for Lie algebraic tools, which allows us to analyze different kind of the time discontinuity cause.