The apparatus and methods of the theory of flows with gains is used for modeling multi-stage investment projects with the possibility of corruption in the paper. The model of the company, implementing a multi-stage investment project with the possibility of corruption is formalized and studied. At each stage of the project its capital intensity is increased as a result of current investment, or is decreased from the corrupt activities of persons involved in the project. Multi-stage project is presented as a network in this paper. The problem for finding the maximum capital intensity at the final stage of its execution is solved. Maximum capital intensities found are used for calculating a compromise solution of the problem implementation of the investment project involving a finite set of agents. Numerical example is solved for the task implementation of the investment project involving three agents.