In the near-Earth magnetotail region the magnetic geometry becomes nonaxisymmetric. Field line resonances (FLR) are studied in such a system. The effects of nonaxisymmetry imply that the azimuthal wavenumber is no longer invariant on each magnetic shell, unlike in an axisymmetric geometry. In this numerical simulation study we investigate how geometric asymmetry affects the ansatz of FLR theory that any radial oscillations are asymptotically damped and transfer wave energy to shear standing modes. It is found in our numerical results that the FLR persist in such nonaxisymmetric cases. The oscillations corresponding to these shear modes are tangential to the ambient Alfven speed surface. It is suggested that the Alfven speed surface can be very useful in establishing a local coordinate system to define the wave polarization. The direction normal to the local Alfven speed gradient is found to be similar to the radial direction in an axisymmetric case, while the tangential direction is similar to the azimuthal direction. In addition, we examine the effects of the finite ionospheric dissipation on the formation of FLR and field-aligned currents.