Phase transition and high-temperature properties of rare-earth niobates (LnNbO(4), where Ln=La, Dy and Y) were studied in situ at high temperatures using powder X-ray diffraction and thermal analysis methods. These materials undergo a reversible, pure ferroelastic phase transition from a monoclinic (S.G. I2/a) phase at low temperatures to a tetragonal (S.G. I4(1)/a) phase at high temperatures. While the size of the rare-earth cation is identified as the key parameter, which determines the transition temperature in these materials, it is the niobium cation which defines the mechanism. Based on detailed crystallographic analysis, it was concluded that only distortion of the NbO4 tetrahedra is associated with the ferroelastic transition in the rare-earth niobates, and no change in coordination of Nb5+ cation. The distorted NbO4 tetrahedron, it is proposed, is energetically more stable than a regular tetrahedron (in tetragonal symmetry) due to decrease in the average Nb-O bond distance. The distortion is affected by the movement of Nb5+ cation along the monoclinic b-axis (tetragonal c-axis before transition), and is in opposite directions in alternate layers parallel to the (010). The net effect on transition is a shear parallel to the monoclinic [100] and a contraction along the monoclinic b-axis. In addition, anisotropic thermal expansion properties and specific heat capacity changes accompanying the transition in the studied rare-earth niobate systems are also discussed.