Normal moveout (NMO) velocity is a commonly used tool in the seismic industry nowadays. In 3D surveys, the variation of the NMO velocity in a horizontal plane is elliptic in shape for the anisotropy or heterogeneity of any strength (apart from a few exotic cases). The NMO ellipse is used for Dix-type inversion and can provide important information on the strength of anisotropy and the orientation of the vertical symmetry planes, which can correspond, for example, to fractures’ orientation and compliances. To describe a vertically fractured finely layered medium (the fracture is orthogonal to the layering), an anisotropy of orthorhombic symmetry is commonly used. In areas with complicated geology and stress distribution, the orientation of the orthorhombic symmetry planes can be considerably altered from the initial position. We have derived the exact equations for the NMO ellipse in an elastic tilted orthorhombic layer with an arbitrary orientation of the symmetry planes. We have evaluated pure and converted wave modes and determined that the influence of the orientation upon the NMO ellipse for all the waves is strong. We have considered acoustic and ellipsoidal orthorhombic approximations of the NMO ellipse equations, which we used to develop a numerical inversion scheme. We determined that in the most general case of arbitrary orientation of the orthorhombic symmetry planes, the inversion results are unreliable due to significant trade-offs between the parameters. We have evaluated S-wave features such as point singularities (slowness surfaces of the split S-waves cross) and triplications (due to concaveness of the individual S-wave mode slowness surface) and their influence on the NMO ellipse.