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We describe contact-resonance atomic force microscopy (AFM) methods to quantitatively measure Poisson’s ratio ν or shear modulus G at the same time as Young’s modulus E. In contact-resonance AFM, the frequencies of the cantilever’s resonant vibrations are measured while the tip is in contact with the sample. Simultaneous measurement of flexural and torsional vibrational modes enables E and ν to be determined separately. Analysis methods are presented to relate the contact-resonance frequencies to the tip-sample contact stiffness, which in turn determines the sample’s nanoscale elastic properties. Experimental results are presented for a glass specimen with fused silica used as a reference material. The agreement between our contact-resonance AFM measurements and values obtained from other means demonstrates the validity of the basic method.