We describe a dynamic atomic force microscopy (AFM) method to map the nanoscale elastic properties of surfaces, thin films, and nanostructures. Our approach is based on atomic force acoustic microscopy (AFAM) techniques previously used for quantitative measurements of elastic properties at a fixed sample position. AFAM measurements determine the resonant frequencies of an AFM cantilever in contact mode to calculate the tip-sample contact stiffness k *. Local values for elastic properties such as the indentation modulus M can be determined from k * with the appropriate contact-mechanics models. To enable imaging at practical rates, we have developed a frequency-tracking circuit based on digital signal processor architecture to rapidly locate the contact-resonance frequencies at each image position. We present contact-resonance frequency images obtained using both flexural and torsional cantilever images as well as the corresponding vertical contact-stiffness (k *) image calculated from flexural frequency images. Methods to obtain elastic-modulus images of M from vertical contact-stiffness images are also discussed.