Maximum and minimum horizontal stresses, and horizontal to overburden stress ratio, are estimated using radial profiles of shear moduli. Inversion enables estimation of maximum and minimum horizontal stresses using radial profiles of three shear moduli associated with an orthogonal set of axes defined by the three principal stress directions. Differences in the far-field shear moduli are inverted together with two difference equations obtained from the radial profiles of the dipole shear moduli C44 and C55, and borehole stresses in the near-wellbore region. The horizontal to overburden stress ratio is estimated using differences in the compressional, dipole shear, and Stoneley shear slownesses at two depths in the same lithology interval where the formation exhibits azimuthal isotropy in cross-dipole dispersions, implying that horizontal stresses are nearly the same at all azimuths. The overburden to horizontal stress ratio in a formation with axial heterogeneity may also be estimated using the far-field Stoneley shear modulus C66 and dipole shear modulus C55 together with the radial variation of the dipole shear modulus C55 caused by near-wellbore stress concentrations.