Untwinned single phase thin films of multiferroic orthorhombic TbMnO3 are deposited by pulsed laser deposition on (110)-oriented NdGaO3 and YAlO3 substrates. X-ray diffraction measurements show that these films grow with a (110)-expitaxy on both substrates and the (110)-plane of a film shows a more square-like distortion imposed by the underlying substrate. Therefore, these films are under tensile strain along the [001] direction on NdGaO3. In the case of TbMnO3 on YAlO3, the film shows an unexpected tensile strain also along [001] 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.