Proposed was a reliability model of the network project as a complex technical system where the probability of failure-free execution of an activity (project component) was used as the quantitative index of its reliability, and the resulting guaranteed lower estimate of the project, as its reliability index. This approach underlies the formulation of the problem of scheduling not only under resource constraints, but also with regard for the project reliability index. Consideration was given to minimization of the project execution time (main criterion) in terms of the constrained cost and estimate of the project reliability index, as well as in terms the cost in the determinate network model of the project (second criterion) where project reliability satisfies the guaranteed lower bound both for the OR-network and the special case of the AND-network. This approach enabled formulation of the scheduling problem not only under the resource, but also reliability constraints.