Riveting and bolting are common assembly methods in aircraft production. The fasteners are installed immediately after hole drilling and fix the relative tangential displacements of the parts that took place. A proper fastener sequence installation is very important because a wrong one can lead to a “bubble-effect” when gap between parts after fastening becomes larger in some areas rather than being reduced. This circumstance affects the quality of the final assembly. For that reason, the efficient methods for determination of fastening sequence taking into account the specifics of the assembly process are needed. The problem is complicated by several aspects. First of all, it is a combinatorial problem with uncertain input data. Second, the assembly quality evaluation demands the time-consuming computations of the stress–strain state of the fastened parts caused by sequential installation of fasteners. Most commonly used strategies (heuristic methods and approximation algorithms) require a large number of computational iterations what dramatically complicates the problem. The paper presents the efficient methods of fastener sequence optimization based on greedy strategy and the specifics of the assembly process. Verification of the results by comparison to commonly used installation strategies shows its quality excellence.