Abstract: Based on the structural features of rivets, an eigenfunction expansion approach is used to analyze the stress singularities in the neighborhood of contact interfaces in cylindrical coordinates. The expressions of the three-dimensional asymptotic stress and displacement fields in the vicinity of the circumferential line are established. A group of non-linear characteristic equations are established under various boundary conditions of displacement and stresses of an assembly with a rivet in a bi-layer plate, based on which the orders of stress singularity, displacement and stress angular variation functions are determined. In the benchmark example, the results show that the eigenfunction expansion approach is valid for estimating the order of stress singularity in the cylindrical coordinates by comparing with the finite element method. In the numerical examples, the stress singularities in three-dimensional contact boundaries of riveted assemblies with flat, countersunk and universal head rivets are analyzed, and the effects of rivet materials, geometrical shapes and friction coefficients on the orders of stress singularities and stress angular variations are investigated.