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This work aims at completing the development of local mechanical spectroscopy as initiated by F. Oulevey during his thesis. More precisely, the measurement of the amplitude and phase lag of the strain as a function of the applied stress frequency bas to be settled. Parallel to the development of the technical aspects making such an acquisition possible, the model used to analyze the measured quantities is modified in order to describe the studied system more realistically. The local mechanical spectrometer is based on an Atomic Force Microscope (AFM) using an optical method to detect the deflection of the lever. The stress is applied locally on the sample by a transducer fixed at the base of the cantilever. The bandwidth of the microscope' s electronics does not allow one to detect the cantilever movement at frequencies higher than the MHz. Two different approaches are followed to overcome this limit. The first approach exploits the nonlinearity of the contact to down-convert, via mechanical mixing, the high-frequency signals into low-frequency ones. This work demonstrates the feasibility of this technique, as well as its limits, mainly due to the difficulty to analyze confidently the obtained results. The second approach takes advantage of the stroboscopic detection of the movement of the cantilever. The intensity of the laser used to detect the deflection of the cantilever is modulated at a frequency close to the applied stress frequency. The amplitude of the signal recorded at the difference frequency corresponds then to the high-frequency amplitude of the cantilever movement. The frequency range attainable with this method is only limited by the bandwidth of the transducer providing the excitation. The model connecting the measured quantities (strain amplitude and phase lag) to the desired mechanical properties (elasticity and damping) consists in a beam clamped at one end, with a tip attached at some point along its length. The tip itself is connected to the sample via a spring and a dashpot in parallel, representing the normal interaction, and a spring and a dashpot in parallel representing the interaction in the plane of the sample. Combined with the stroboscopic detection, this model enables one to quantitatively determine the elastic modulus of stiff samples. Many results obtained on a wide range of samples exhibiting very diverse mechanical properties are presented. They demonstrate the validity of the stroboscopic approach, which combines simplicity of use and efficiency.