Lateral forces between the tip of a force microscope and atomic-scale features on the surface of a sample can be accurately measured in a noncontact mode. Feedback-controlled excitation of the torsional eigenmode of a rectangular cantilever beam forces the tip to oscillate parallel to the surface. Forces of the order of 0.05 nN have been detected when the tip approaches a step or a sulphur impurity. The method can also be used to study the energy dissipation in the range where a tip-sample contact is formed.