An approach for combined imaging of elastic and electromechanical properties of materials, referred to as piezoacoustic scanning probe microscopy (PA-SPM), is presented. Applicability of this technique for elastic and electromechanical imaging with nanoscale resolution in such dissimilar materials as ferroelectrics and biological tissues is demonstrated. The PA-SPM signal formation is analyzed based on the theory of nanoelectromechanics of piezoelectric indentation and signal sensitivity to materials properties and imaging conditions. It is shown that simultaneous measurements of local indentation stiffness and indentation piezocoefficient provide the most complete description of the local electroelastic properties for transversally isotropic materials, thus making piezoacoustic SPM a comprehensive imaging and analysis tool. The contrast formation mechanism in the low frequency regime is described in terms of tip-surface contact mechanics. Signal generation volumes for electromechanical and elastic signals are determined and relative sensitivity of piezoresponse force microscopy (PFM) and atomic force acoustic microscopy (AFAM) for topographic cross-talk is established.