We have studied the three first symmetric out-of-plane flexural reso- nance modes of a goalpost silicon micro-mechanical device. Measurements have been performed at 4.2 K in vacuum, demonstrating high Qs and good linear prop- erties. Numerical simulations have been realized to fit the resonance frequencies and produce the mode shapes. These mode shapes are complex, since they involve distortions of two coupled orthogonal bars. Nonetheless, analytic expressions have been developed to reproduce these numerical results, with no free parameters. Owing to their generality they are extremely helpful, in particular to identify the pa- rameters which may limit the performances of the device. The overall agreement is very good, and has been verified on our nano-mechanical version of the device.