General relations are obtained for the determination of radial and tangential components of displacements and gravitational potential variations at the Earth's surface due to tidal forces for a model with a horizontally inhomogeneous distributions of elastic moduli. Model calculations are performed to estimate the effects of local and regional inhomogeneities of elastic moduli specified in regions of simple configurations on tidal variations in gravity, tilts and deformations. As distinct from gravity data, data on tidal tilts and deformations can provide significant constraints on local inhomogeneities of elastic moduli in the immediate vicinity of an observation point. Results of model calculations show that the phases and amplitudes of tidal tilts and deformations change by 10-15% in the vicinity of a soft inclusion in which the shear modulus is smaller than its value in the surrounding medium by 20-30%. Anomalies of such a contrast can be detected over several months of continuous tidal observations.