The use of third-party ready-made solutions to perform special computing tasks (SCT): processing text arrays in a natural language, the use of cryptography methods in data transmission networks, machine learning in solving applied problems, scientific computations and many other ones is a common practice in modern development of software systems. However, the use of third-party ready-made software solutions often leads to their poor optimization for parallel and distributed operation and to the difficulty in vertical and horizontal scaling, impossibility of modifying a solution, e.g., due to its legal protection, etc. In order to solve these problems, an asynchronous actor model can be used that facilitates developing software for processing special computing tasks. In addition, an asynchronous actor model allows parallel processing of input tasks, provides asynchronous operation, and extends its functionality to third-party ready-made solutions, that it is impossible or forbidden to modify to meet user’s or optimization requirements. Methods, algorithms, and the entire logic of asynchronous actor operation involve transitions of actors from one state to another under the effect of input messages and returning the results of processed tasks to the frame system. This allows setting an automatic grammar and for using methods and approaches for developing software systems based on finite-state automata. The asynchronous actor operation scheme is represented by a directional state graph, which allows using the mathematical apparatus of the finite-state automaton theory (the Mealy model) to describe the same. The developed model is convenient for designing and organizing the SCT processing using computer systems. The use of the asynchronous actor model makes it possible, in special operation modes, to increase the performance of poorly optimized SCT without modifying the same, as compared to task processing without using the asynchronous actor model.