Torsional oscillations of six single sunspot umbrae are investigated from observations of the longitudinal magnetic field and velocity field in the photospheric line Fe I λ 525.3 nm. All three components of the magnetic field and velocity field are reconstructed from their line-of-sight components. The periods of the umbra oscillations correspond to 2.2—7.1 days. The initial phases of the oscillations are distributed over the interval from 0 to 2π. The azimuthal velocity calculated from the velocity field is much more than the azimuthal velocity measured from photoheliograms. The azimuthal velocity oscillation phase is ahead of the phases of all other component oscillations of both vectors. The period of oscillations increases with latitude of a sunspot. The magnetic energy of oscillations exceeds their kinetic energy by a factor up to 1000 (when the plasma density is 10^-4 kg/m³).