The implementation of three-dimensional (3D) nano-objects as building blocks for the next generation of electro-mechanical, memory and sensing nano-devices is at the forefront of technology. The direct writing of functional 3D nanostructures is made feasible by using a method based on focused ion beam induced deposition (FIBID). We use this technique to grow horizontally suspended tungsten nanowires and then study their nano-mechanical properties by three-point bending method with atomic force microscopy. These measurements reveal that these nanowires exhibit a yield strength up to 12 times higher than that of the bulk tungsten, and near the theoretical value of 0.1 times the Young's modulus (E). We find a size dependence of E that is adequately described by a core-shell model, which has been confirmed by transmission electron microscopy and compositional analysis at the nanoscale. Additionally, we show that experimental resonance frequencies of suspended nanowires (in the MHz range) are in good agreement with theoretical values. These extraordinary mechanical properties are key to designing electro-mechanically robust nanodevices based on FIBID tungsten nanowires.