Selecting from a pool of interdependent projects under certainty, when faced with resource constraints, has been studied well in the literature of project selection problem. After briefly reviewing and discussing popular modeling approaches for dealing with uncertainty, this paper proposes an approach based on chance constrained programming and utility theory for a certain range of problems and under some practical assumptions. Expected Utility Programming, as the proposed modeling approach, will be compared with other well-known methods and its meaningfulness and usefulness will be illustrated via two numerical examples and one real case.