This study is concentrated on the natural frequencies and mode shapes of a simple three-member space frame coupled with a dynamic vibration absorber. The dynamic vibration absorber is modeled as a six-degree-of-freedom mass-spring system. For the first time, the free vibration of an elastic structure with a six-degree-of-freedom mass-spring system is found. Each member of the space frame has uniform mechanical and geometrical properties, but these may differ from one member to another. The exact result of this complex problem is obtained via analytical scheme and finite element method. All effects of the axial and torsional deformations and also in- and out-of-plane bending are taken into account. This formulation includes eighteen differential equations along with thirty six boundary and compatibility conditions. Comparison of the results by both approaches mentioned above, illustrates the accuracy of our solutions. Findings are useful benchmarks for the natural frequencies and mode shapes of the space frame coupled with a dynamic vibration absorber.