The aim of the work is to improve the quality of the computational process that solves the problem, due to its modeling and debugging based on the Petri net. The quality of the computational process is understood as the absence of errors (looping, paralysis, unreliability of some fragment, etc.) and its optimization according to the criterion of minimum complexity.The new approach to the analysis of the computational process, based on preliminary modeling by Petri nets of both fragments of computational processes and complete computational processes, is proposed. This will reveal many errors at the stage of modeling the computational process. The computational process is considered as a set of macrooperations, which are functionally, completed operations of various hierarchical levels. To locate macrooperations in a computational process, it is decomposed into elementary (basic) computational constructions. A statement that any computing process can be constructed on the basis of a relatively small number of macrooperations is formulated. To implement the new approach, the task of developing a method for constructing a Petri net according to a given computational process is formulated and solved. The essence of the proposed method consists in dividing the computational process into macrooperations, building a Petri net fragment for each macrooperation, modeling all fragments, assembling a complete Petri net from network fragments and modeling it. To implement the method, a procedure for constructing a computational process model is being developed. The stages of this procedure are described: decomposition of the computational process into macrooperations according to the proposed rules, translation of macrooperations into fragments of the Petri net and their modeling, collection of the complete Petri net by the proposed rules, and modeling the resulting Petri net. The results of the implementation of all stages of the procedure are recorded in the library, the aim of which is the accumulation of knowledge about the computational processes corresponding to them Petri nets and modeling results. This allows us to simplify the process of modeling a new computing process through the use of already debugged fragments. If the computational process contains errors or is not optimal, it is corrected, which allows to improve its quality according to the above criteria. By the example of sorting by inserts, the correctness of the operation of the constructed Petri net using the declared method is experimentally confirmed.