This paper presents a new method for critical path (CPM) scheduling that optimizes project duration in order to minimize the project total cost. In addition, the method could be used to produce constrained schedules that accommodate contractual completion dates of projects and their milestones. The proposed method is based on the well-known "direct stiffness method" for structural analysis. The method establishes a complete analogy between the structural analysis problem with imposed support settlement and that of project scheduling with imposed target completion date. The project CPM network is replaced by an equivalent structure. The equivalence conditions are established such that when the equivalent structure is compressed by an imposed displacement equal to the schedule compression, the sum of all member forces represents the additional cost required to achieve such compression. To enable a comparison with the currently used methods, an example application from the literature is analyzed using the proposed method. The results are in close agreement with those obtained using current techniques. In addition, the proposed method has some interesting features: (i) it is flexible, providing a trade-off between required accuracy and computational effort, (ii) it is capable of providing solutions to CPM networks where dynamic programming may not be directly applicable, and (iii) it could be extended to treat other problems including the impact of delays and disruptions on schedule and budget of construction projects.Key words: construction scheduling, time–cost trade-off, project cost optimization, scheduling with constraints, project acceleration.