Elliptical nanowires and nanotubes, due to the anisotropy of their shape, have unique physical properties that can be utilized to create new electronic nanostructures with pronounced anisotropy of intensity and polarization of emitted or absorbed light [1]. In this study, the effect of a tilted electric field on the oscillator strength of intraband electron quantum transitions in an elliptical GaAs nanowire and an elliptical AlGaAs/GaAs nanotube is investigated in effective mass approximatin. Two types of nanotubes were considered. The first is nanotubes, the cross-section of which is confined by two ellipses with the same focal length. In this case, as in the case of an elliptical nanowire, in the absence of an electric field, exact solutions of the Schrödinger equation can be obtained using even and odd angular and radial Mathieu functions. These solutions form the basis for the expansion of the wave functions of the electron taking into account the influence of the electric field. If the electric field is directed along the major axis of the ellipse, then the even/odd wave functions retain their property of symmetry with respect to the major axis of the ellipse, and therefore the decomposition of the wave function occurs only in the even/odd states of the basis functions. In all other directions of the electric field, a full set of basis functions is used. Nanotubes of the second type have the same wall thickness along the major and minor semi-axis of the ellipse. For such nanotubes, exact solutions of the Schrödinger equation cannot be obtained even in the absence of an electric field. Therefore, their research was carried out using the finite element method using the COMSOL Multyphisics. The dependencies oscillator strength of intraband electron quantum transitions for x- and y-polarized light on the orientations of the external electric field at different ellipticities are obtained.