Developing a suitable mathematical model for the system under study is an important challenge in scientific and engineering research, especially when nothing is known except the inputs and outputs of the system. This problem is generally referred to as the identification problem. Different evolutionary computations based on evolutionary processes in the nature have shown high effectiveness in solving such problem. This paper is devoted to the development and study of the algorithm for identification of dynamic systems based on the processing of observed data. The identification algorithm is based on the method of genetic programming. The obtained mathematical model of the dynamic system is represented in the form of differential equations. Computer testing of the developed algorithm in Python environment using DEAP showed high efficiency. In particular, the trade-off between the accuracy and complexity of the identified mathematical models is analyzed. Also, the influence of noise on the genetic programming algorithm has been studied. The results show that the genetic programming method has good reliability when used for identification, but there is still room for improvement.