Known approaches to project team management typically rely on intuitive decisions of project managers, rather than regularities and laws of role interaction between project participants. To resolve this contradiction, it is necessary to generalize and develop applied aspects of the use of the Markov chains to represent and model the projects as a system of role communications in a project team. To construct a Markov chain, we used a well-known role model of a project team by R. Belbin, which represents the structure of project participants only qualitatively. We developed a graphical representation of the cognitive structure of the role model, which is similar to a directed graph with vertices – states of the project, and arcs that represent communication links between project participants. Construction of the graph enables us to create a matrix of transition probabilities for communications of a project. To finish the method of transformation of a role model, it is necessary to pass to the development of analytical stepwise method to solve the system of equations of the Markov chain with discrete states and time. It is shown that iterative solution of the system of equations of the Markov model forms a "trajectory" of development of virtual or actual projects based on the characteristics of role communications. The practical aspects of assessment of effectiveness of the "trajectory" of projects development were explored using the developed Markov model. Evaluation of results of change in the distribution of probabilities of states of a project in coordinates of probabilities of states of the system in steps revealed a significant effect on the progress and effectiveness of a project in the case of variation of competences of only one member of the team project. These results reflect the essential property of teamwork: effectiveness of projects depends on the coherence of roles of all project performers