One of the tasks of a complex nonlinear dynamic system analysis in the case of multystability there is determination of initial conditions, corresponding to one or another oscillation regime. At the decision of this task the areas of initial conditions corresponding to one oscillation regime are selected on a phase plane, i.e. constructing of basins of attraction of this regime. One of the basins of attraction construction methods is a method of cellular mapping (cell-to-cell mapping). This method is behaves to the class of “brute force” and its application requires the considerable expenses of machine time. Some changes, allowing accelerating his work, are ma de in realization of classic method. In the paper descriptions of algorithms of basins of attraction construction and results of multystability analysis are presented for three systems: discrete system of Henon, system with cube elastic force, system with bilinear elastic force.