A method for deriving analytical descriptions of computing algorithms is developed on the example of the problem of identification. Traditional algorithms cannot be used in conditions of ill-conditioned almost singular systems of equations typical for identification of dynamic processes. More stable algorithm, which was not applied because of mathematical difficulties of its realization, has been developed. These difficulties have been overcome due to use of symbolical combinatory models (SC models), allowing to form analytical descriptions of algorithms; the elements of inverse matrix have been expressed as function of parameters of dynamic process. It is proved that SC models are effective means for reducing the complexity of algorithms and their analytical descriptions. Results can be recommended for procedures of imitation modelling with the purpose of testing the usability of algorithms in problems of processing of flight information of aerospace systems.