A 3D single-particle-tracking (SPT) system was developed based on two-photon excitation fluorescence microscopy that can track the motion of particles in three dimensions over a range of 100 mum and with a bandwidth up to 30 Hz. We have implemented two different techniques employing feedback control. The first technique scans a small volume around a particle to build up a volumetric image that is then used to determine the particle's position. The second technique scans only a single plane but utilizes optical aberrations that have been introduced into the optical system that break the axial symmetry of the point spread function and serve as an indicator of the particle's axial position. We verified the performance of the instrument by tracking particles in well-characterized models systems. We then studied the 3D viscoelastic mechanical response of 293 kidney cells using the techniques. Force was applied to the cells, by using a magnetic manipulator, onto the paramagnetic spheres attached to the cell via cellular integrin receptors. The deformation of the cytoskeleton was monitored by following the motion of nearby attached fluorescent polystyrene spheres. We showed that planar stress produces strain in all three dimensions, demonstrating that the 3D motion of the cell is required to fully model cellular mechanical responses.