In this work, a high-resolution atomic force acoustic microscopy imaging technique is developed in order to obtain the local indentation modulus at the nanoscale level. The technique uses a model that gives a qualitative relationship between a set of contact resonance frequencies and the indentation modulus. It is based on white-noise excitation of the tip–sample interaction and uses system theory for the extraction of the resonance modes. During conventional scanning, for each pixel, the tip–sample interaction is excited with a white-noise signal. Then, a fast Fourier transform is applied to the deflection signal that comes from the photodiodes of the atomic force microscopy (AFM) equipment. This approach allows for the measurement of several vibrational modes in a single step with high frequency resolution, with less computational cost and at a faster speed than other similar techniques. This technique is referred to as stochastic atomic force acoustic microscopy (S-AFAM), and the frequency shifts of the free resonance frequencies of an AFM cantilever are used to determine the mechanical properties of a material. S-AFAM is implemented and compared with a conventional technique (resonance tracking-atomic force acoustic microscopy, RT-AFAM). A sample of a graphite film on a glass substrate is analyzed. S-AFAM can be implemented in any AFM system due to its reduced instrumentation requirements compared to conventional techniques.