Untwinned single phase thin films of multiferroic orthorhombic TbMnO₃ are deposited by pulsed laser deposition on (1 1 0)-oriented NdGaO₃ and YAlO₃ substrates. X-ray diffraction measurements show that these films grow with a (1 1 0)-expitaxy on both substrates and the (1 1 0)-plane of a film shows a more square-like distortion imposed by the underlying substrate. Therefore, these films are under tensile strain along the [0 0 1] direction on NdGaO₃. In the case of TbMnO₃ on YAlO₃, the film shows an unexpected tensile strain also along [0 0 1] contrary to expectations. X-ray reciprocal mapping confirms that with increasing thickness the film lattice parameters relax towards bulk values. In addition, an increase in mosaicity is also observed.